OK I am back! @spacewitch10 (just in case it doesn't notify you otherwise)
I think basically you're getting mixed up with several different ideologies, and it might make sense to have those separated out to help you make sense of it and work out where you want to go from here.
I think there are two things that need to be separated out. Root cause of behaviour, and the appropriate parental role.
Root cause of misbehaviour
There are two conflicting theories I can see coming through in your post here - one is the theory of behaviourism which is the assumption that children misbehave (which is behaviour that goes against accepted norms) because it is fun for them or it gets them what they want. The scientific theory says that all humans and some animals are influenced by antecedents (something that prompts the behaviour) and consequences (which can be rewarding or punishing - just whatever happens as a result of the behaviour).
According to behaviourism, the way to change behaviour is to change these two things, mostly the consequence part, ie how you react to behaviour is absolutely important and it is important to be consistent in your response so that children learn what is acceptable and unacceptable behaviour.
The other is the theory of dysregulation / stress behaviour (or "behaviour is communication") which says that misbehaviour is actually stress behaviour, ie it is unconscious and it comes from their underlying state. In order to solve stress behaviour, in the moment you would co-regulate to bring the child down from dysregulation back to calm, and longer term you look to teach the child better awareness of their own regulation, tools for self-regulation, and you look to manage the environment around them to reduce stress (and teach them to do this for themselves), which might involve things like identifying skills they are lacking and supporting them directly with those skills.
Parental role
I can also see two conflicting senses of parental role in your post. The one that commonly links in with behaviourist ideology is the idea of hierarchy aka adults are higher, socially, in status than children and particularly parents over children. Children are expected to follow directions from adults because adults are in charge. Parents are expected to control children's behaviour (which is why behaviourism links in well) and there is a sort of assumption that if you don't address behaviour then it will get worse and worse over time. It's also quite a zero-sum game thing, where it's like a power struggle - the parent has to "win" because otherwise the child "wins" and if they do then they have lost their place in the hierarchy which is not correct. Adults should be united as this is what helps children understand what the expectations are of them, and what is generally considered acceptable/unacceptable behaviour. It doesn't need to be draconian and harsh - you can be a benign dictator, but you are expected to have the dictator role. Adults make decisions and directions, children follow them.
Then the one which links more commonly with an understanding of dysregulation is more the role of being a mentor or helper. Rather than control the child, you're looking to support and help them to do well which you believe they will do when they are not dysregulated, and if they are not doing well it's because something is going on for them. The adult role is still to keep the child safe and ensure that they get everything they need to grow up safe and healthy, but there is less emphasis on control and authority, more on guidance and support.
---
So you described a situation which began to get stressful. You recognised dysregulation, and misbehaviour, so you addressed this by being calm (good for coregulation, also important for consistency) and stern (which comes more from hierarchy/behaviourism - establishing authority and hinting at disapproval)
Then you said no to a cuddle, as you felt stressed. This fits into the mentor role, in terms of modelling your own self-regulation and personal boundaries. However, remember that when a child is dysregulated, they are much less able to take on board learning type information, so it might not be the best situation to try and use that tool.
You also said you wanted him to comprehend the situation - I don't know what this means - do you mean in the sense of like "Think about/see the effect you have had on me"? Like a natural consequence? I think this comes from a behaviourist ideology.
He then sought comfort from your mum instead. You were thinking "He can get the coregulation from her" - this might work as a solution, if you can explain the dysregulation/coregulation model to her and explain that you wanting space is not about punishment, but about you having a minute.
She was probably thinking "Mum disapproved of that behaviour and has refused a cuddle as a result. I will to or it will totally undermine what message mum is sending". (Behaviourism, hierarchy.)
In your later reply to me you referred to him being rude and disobedient. Rudeness is an interesting one because of course there are types of rudeness which would be relevant between anyone - but I think it comes up in a hierarchical parental role because the child is expected to some extent to be deferential and when they are not, that is seen as rude (often "cheeky" or "disrespectful") and, again, the concept of disobedience is all tied very closely into hierarchy - if you're in charge, and expect your directions to be followed, then not doing this is a problem. Whereas if you're more of a mentor/helper role then disobedience as a concept doesn't really apply in the same way.
With you both being "against him" that is basically right in a hierarchical/behaviourist framework because it's not about you being against HIM, it's about you both being against his behaviour. He is not his behaviour. This is why if you use behaviourism it's important to balance it with lots of positivity and praise and set up opportunities to catch and notice him being good and behaving in the way you want, to build a positive image of himself and encourage him in the mindset that he can be that person who behaves in an acceptable way.
In terms of neurodiversity -
Some ND people are especially tuned in to others' regulation/stress state. So a false calm projected in the pursuit of being consistent and a leader role will not be as effective as if you can get straight into your own self-reg (or take the minute before you address the behaviour) and project real calm, with the point being for your "body to body" communication to help coregulate him back to a state where he can listen and take on board your points.
If you are going to use a behaviourist approach, the recommended approach with ND children is to reduce your use of punitive consequences as far as possible, and when you have to do this then you want to keep it very predictable (e.g. "If you hit people you will lose points from your behaviour chart") and not just make up consequences in the moment, which means weirdly that the "gentle parenting" thing of natural consequences is less effective in this sense.
ND children will also find it harder to infer "lessons" directly from consequences, which is another reason that natural/related consequences are less relevant unless it is very clear and very direct (e.g. refuse to come off game at correct time = lose game time tomorrow.) And again these should be planned and explained in advance. But because they will not learn the "why" directly from the consequence, you have to teach the skill or reinforce the replacement behaviour separately as well.
ND people might be less aware of their tone or vocabulary choices in terms of disrespect/rudeness. If you are going to pull him up on rudeness, it would be helpful to establish whether he actually understands what your expectation is, and whether your expectation changes in different contexts, which might seem obvious to you but could be a mystery to him. This might be something you simply ignore for the time being, or it might be something that you consciously work on and practice with him. (Especially people on the autism spectrum can struggle with concepts like tone and respect).
In fact I think that some ND children really struggle with the entire concept of a hierarchy where they have to adapt their behaviour, tone and wording based on who they are speaking to. Particularly if you have any Demand Avoidance/PDA in the mix because they can find it very difficult to be directed. But for example it can be confusing that you are allowed to say to him "No, stop arguing when I tell you to do something" but he is not allowed to say that to you, or to other children. OTOH some children find it much clearer when these roles are defined and they have set rules and boundaries which are clear to them.
Can you combine the approaches? Possibly. I think that the key to this is to not try to combine them within the moment, which is the ONLY thing I think you're getting tripped up by. You have loads of really good aspects of each approach. You could try specifically focusing on one though rather than trying to use them both together, which won't necessarily work because they have points where they work against each other.
I think if you're going to look into behaviourism, it's important to do this in a very positive, proactive and goal-orientated way as this is very clear. Make a behaviour plan and decide which behaviours to work on. There is a good, free course on Coursera called The ABCs of Everyday Parenting which explains this very well. It has very minimal reliance on punishment and much more of a positive approach in general. The only things I disagree with on the course in relation to ND are that some of the behaviours they use as examples are expressions of emotion (e.g. crying) and I am uncomfortable with this. I don't think that it's a good idea to use behaviourism to discourage expressing emotions - I think this causes masking, which can be harmful to ND people. I also don't like the example used where they try to increase compliance or decrease a behaviour of a child saying no - I tend to think this can also be a problem for ND people because it teaches them to override when they don't feel comfortable with something.
For example, compliance is "When I tell you to do homework, you go and do your homework. When I ask you to come off the game, come off the game." whereas you could just work on those two behaviours (doing homework, coming off the game at a set time) rather than working on compliance. I think this is safer in the context of ND because ND is more likely to present problems with any specific expectation, and "compliance" as a goal is much too broad. If you're looking to increase/decrease specific behaviours, then it gives you a chance to work out whether they are actually realistic expectations or whether your child is struggling with an aspect of it and then you can work on that specifically (maybe using Ross Greene's Collaborative Problem Solving, or by looking for the stress factors).
Lastly I don't think it was in the course but I would not use behaviourism to decrease stimming behaviour. Stimming is a way that ND children self-regulate and shouldn't be stopped (you might want to look into what is causing them to feel dysregulated but it might also be absolutely fine, as they are managing this themselves). If their stimming is disruptive to others then it might be something you can address another way or come up with a compromise.
If you are wanting to combine with an awareness of dysregulation, then I think Daniel Siegel's "Connection before Correction" approach is helpful - you can probably look this up online. Be aware that behaviour happening in the grip of dysregulation is not chosen, and trying to correct it in that moment won't be very effective. Coregulate and calm, then have the conversation afterwards and remind of the positive behaviour expectation. Don't pull up on every single bit of dysregulated behaviour, only the behaviours you're actively trying to target as per your behaviour plan.
If you want to pivot directly into the dysregulation/mentor type role instead, some good resources for this are Mona Delahooke, Conscious Discipline, Stuart Shanker, Ross Greene's Collaborative Problem Solving and Zones of Regulation. The key to this one is more about creating an atmosphere of viable safety, which means dropping all of the hierarchical stuff in order to position yourself on his side, and potentially most of the demands/expectations (at least short term) as well.
I know this was a really long post, so I hope it's not overwhelming! I don't think that you have to be perfect at any of this, I certainly am not, but it has definitely helped me to unpick what assumptions I have and which root they are coming from.