OK, a lot to take in, so I will try to throw some thoughts together probably in a bit of a chaotic order (sorry, that's my ADHD).
Screen time - it's such a roulette here - if you can get a handle on his body signs to try and work out if he's calm or stressed, then you might be able to work out what effect the screen time is having on him. Some ND children self-regulate or self-stim with screens but sometimes they are dopamine seeking and they will be sat watching it in this wound up state. Being still and quiet does not necessarily mean that internally, he is calm. Try sitting with him to watch - does he feel tense in his body, is he pushing against you and wriggling, how's his breathing, does he cuddle into you? Do you notice different effects with different kinds of TV - fast paced vs slow, familiar vs new, scenes of conflict/fighting/rescuing/danger can be stressful (even though they are drawn to it) - is there so much visually going on on-screen, are the colours bright and saturated or more muted/realistic? Better or worse with iPad than TV? There is an instagram account called amazing.autistic.abby who had some iPad app suggestions which they like for their autistic daughter. Mostly paid - all the subscriptions totalled up to a ridiculous amount TBH - but might be worth a look if looking to change screen time effect.
I did find with DS1 that absolutely any negotiation or wiggle room in screen time would backfire as he would spend the entire day OBSESSING over whether it was screen time or not yet. Having blanket rules about it's allowed/not allowed at certain times makes this easier because there is just no discussion.
You mentioned your own ND - ADHD or ASD or something else? Medicated? Perimenopause? I do think you're probably having a very proportional response to stress so I don't think there is necessarily anything "wrong" but I am wondering if there's anything which you could get in place for you which might help.
Can't remember if I posted it before but there is this amazing book called When Your Kids Push Your Buttons - it really really helped me.
This may help though I'm a bit reluctant to post as it's paid but you know what - in case you're at that point - I haven't done this particular course but I have done the free primer for it and would definitely consider paying for the full one if we were having to wait so long. https://theotbutterfly.com/bootcamp/
For emotional regulation you basically have three angles to address this from.
Teaching him self-regulation skills - you need to find ways to work these in at positive/fun times, rather than expecting him to learn them in the moment, though. There is this incredible program for schools, called Conscious Discipline. You can adopt a lot of this for your home actually - look at their website/youtube or look for podcasts where the founder Becky A Bailey is talking. I think this is brilliant because what they do is basically teach a load of self-regulation concepts to children in the form of things like action games and songs. They make it fun so that when children access these things in moments of stress it doesn't just feel like this WTF stupid thing you are making him do that he doesn't want to. I also like the way all their tools are designed so that teachers can use them as prompts to remind THEM what to do/say to the children - this works for me too as a parent.
This talk is also great, as is everything on this website/her Facebook page is useful if you are on there, you might not agree with every single post, but there is so much helpful stuff. https://www.occuplaytional.com/2024/02/12/feeling-all-the-feelings-webinar-hosted-by-neurodiversity-ireland/
The second angle is working on your own coregulation skills, which means learning how to self-regulate your own emotions in times of stress - which is REALLY HARD. Particularly when you're struggling with these fears for DS and your family. If you can access therapy at all, preferably trauma-informed, this will probably be useful for you because he is going to be picking up on your body language too and it's just a lot to try and not go into this state because you'll be reacting to him and he'll be reacting to you and it is going to go around and around in a feedback loop. This is probably the hardest part. Reframing can help, but probably isn't going to override deep-seated fears and memories and learned protective responses. You can do some learned physical tricks to present a regulated front in the moment for DS - get low and slow, get close, speak quietly, slowly, calmly, soften your eyes/face, slow your breathing very deliberately and obviously, drop any expectations of him doing whatever it is that you asked, focus on preventing harm and getting him back to a calmer space.
The third and arguably most important will be reducing his stressors overall within the environment. That is tricky because you might not really know what exactly they are. But in general you can try reducing demands, reducing sensory input (e.g. background noise, bright or changing light), creating separate play spaces for him and his sister, keep meals close together and "safe" foods you know he's likely to eat, experimenting with adding in some sensory stimulus to see what helps - this might be a good starting point? https://www.occuplaytional.com/2023/12/04/a-proprioception-primer/
Something which was quite helpful for me was a suggestion by the OT Butterfly in the free version of the course I linked above which is to keep a diary over a few days. I used a sort of "Zones of regulation" shorthand and just whatsapped myself, using the coloured heart emojis at the beginning of the text to denote what "zone" I felt he was in which I denoted as follows:
💚 regulated/appropriate energy for the situation
🧡 dysregulated - being "naughty" or silly or disruptive
❤️ meltdown/explosion
💛 what I started to see as "subtle" dysregulation signs, ie he's not actually doing anything wrong or that I could put my finger on exactly, but it's giving me that warning sense because I can tell he's ramping up.
💙 this is for sleepy in zones of regulation but I didn't find I used it very much.
After the heart, I would then just write a few words about what I noticed (e.g. stiff muscles) and/or what we were doing, or what the situation was (e.g. playing trains together; or - hit brother because brother took his lego piece).
Because it's whatsapp, it has a time stamp and it's easy to access as my phone is to hand. So I could look back over the log I'd created and see:
There are actually green hearts. I had this sense that he was NEVER calm but that was not exactly true.
What kind of activities tended to give him more green hearts
What kind of experiences tended to lead to more yellow or orange
That there are times of day which typically have more green or more yellow/orange.
Self-Reg by Stuart Shanker is also very good though I didn't really understand it just from reading the book - I had to listen to a lot more of his talks, podcast interviews etc. Basically for emotional regulation I've just done stuff like run a search for any terms like this on a podcast app and listened to anything I could get hold of and pieced it all together bit by bit. I think the most useful thing I got from this is the idea that stress is, biologically, anything which makes the brain burn glucose, which means that you can have a sort of mental image of a brain which has a fuel resource from which several different processes all run off.
When you're running one process very very hard, for example a child who has sensory issues might be running their sensory processing very hard, it reduces capacity in all the others so social, cognitive, empathy, problem solving etc. And vice versa. If they are working very hard at social because social situations are stressful for them, it may reduce their capacity to process sensory input.
Reduced capacity means both that they are less able to do it, so for example a child who seems fine at reading in one situation when they are totally calm and supported, but in another situation where there is stress on their other systems, it is overloading their overall capacity and they can't access the energy they need to concentrate on reading. The teacher/parent might get frustrated because they know that the child CAN do this and not understand that in this scenario they can't (because they need more brain fuel which is currently being diverted to different processes).
But it can ALSO mean that they are getting pushed closer to that pressure-cooker scenario where they blow up. Where for example a sensory input like clothing is something they can cope with in one scenario, but another time when they have stress build up from other things the act of putting a coat on feels so intolerable to them that it pushes them right into meltdown.
The accounts I follow online which talk the most about self-regulation are occupational therapists. Maybe there's a possibility to access private OT?