First of all you didn't scare me off @Nepmarthiturn , I tackle these issues day in day out in my voluntary role, I wanted to wait until I was on my laptop so I could break things down properly.
Ofsted etc is not reliable, the mainstream college DD went to is seen as a great college, they have a whole thing about extra support for those who are ND..absolute lies. DD wasn't even there for half a term and was suicidal because they refused to follow her EHCP. We were very lucky that there is a local specialist mental health school that absolutely changed her life, I just wish they could help more kids. Also, the reason that support isn't happening for your kids is money, it always boils down to money. Even with an EHCP schools/colleges will try their best to avoid anything that will cost them money (or that they think will cost them money). Having said that I absolutely recommend starting the EHCP process now for both of your kids (you don't have to wait for the school to do it you can do it yourself). Please have a look at this link it will guide you through doing a parent request for an assessment - https://www.ipsea.org.uk/ehc-needs-assessments Also as @Wishingitcolder said an EHCP opens up a lot more education options other than just mainstream.
For evidence to go in with the assessment request, your posts are a very good start but I'm sure you can add a lot more.
For your son;
Struggles a lot with social relationships (you could summarise all of the problems he's had with the other kids) and the school is not implementing any strategies to assist him with his social skills (or tackling the nasty behaviour/violence)
Struggling to sit at a desk all day, OT report states regular breaks including movement breaks but they are not happening
Extra support with handwriting is needed but is not being offered
Struggles with executive function but is not receiving reasonable adjustments, even with cost-free suggestions(like the visual chart) from you they are not implementing anything to help him
Struggles to eat as fast as the other kids, and requires extra time, no adjustment is made for this result is that he is hungry and unable to concentrate properly
Is not being pushed academically, he is bored as they are not willing to adjust the work to his level
Point out that because his additional needs are not being met he has school refused in the past and he is at risk of this becoming a regular occurrence, especially as he grows and the demands of school life increase.
For your daughter;
Delayed start to reception due to emotional disregulation, point out that emotionally she is behind her peers and vulnerable, mention that her excitement for starting school has turned to dread and anxiety due to needs not being met. All the work you have done on emotional regulation is being undone.
Adjustments that were agreed during the transition meetings are not happening, such as regular breaks and support aids, meaning she is having even more meltdowns at home but has had them during school. Point out that she is very good at masking so for her to meltdown whilst still at school shows how much she is struggling.
School staff were told by both yourself and nursery staff that she required support with sensory and social issues but needs pushing academically as she is beyond her peers already and none of it is happening.
She feels trapped in the classroom and has no trust in staff, she is on the cusp of school refusing already.
The way the school has reacted to everything is screaming red flags to me(assuming same school for both kids?), is changing schools a possibility? See if you have a local SEN parent forum and find out from other local parents which schools actually try to help and which to avoid (same with secondary get ahead with that now).
As you have another meeting coming up over your daughter you need to get legal with them. Point out to them that they are discriminating against your kids by not making reasonable adjustments. NAS has some info and examples that may help - https://www.autism.org.uk/advice-and-guidance/topics/education/resolving-differences/england/disability-discrimination
Do go in with strategies that won't cost them anything (or hopefully take too many resources) so it's not all negative. Say you get it, it's difficult trying to accommodate 30+ kids needs with just 1 teacher, so here are things they can do that will help your child(ren) without being a drain on resources. For example things like movement breaks are such a simple one to implement They could ask your son/daughter to do things like give out/collect work books, that's a movement break that gets them out of their chair without being disruptive.
Also ask them if they are doing assess, plan, do review, if not, why not, your children have diagnosed special educational needs and that is a standard practice.
If you want anymore specific advice drop me a PM, I'm so sorry you and your kids are going through this, unfortunately, this is how the system works, they let our kids struggle and develop MH issues before they step in, all to save themselves some money. Silly thing is if they just put simple things in place from the get-go they wouldn't end up with such traumatised kids which then costs them ridiculous amounts to provide education/support.