You could be writing about my life OP.
I don't wish to piss on your cornflakes but it can take a long time battling the LA for a specialist placement, and it can often be not very straightforward, with a lot of absence from school, not being in a named school at all, or specialist not being the right fit either.
Your children are a joint responsibility though, so your husband needs to step up here. Your life deserves fulfillment and purpose beyond the household and caring duties.
Just because nobody at his current place works part time, it doesn't mean he can't apply for flexible working.
There was a reform with the introduction of the Employment Rights Act 2025 that states employees can request flexible working from day 1, make 2 requests per year, a consultation is required before refusal, and the employee does NOT have to explain the impact to the business that their request will make.
Employers can only refuse if the request impacts one or more of these areas:
Burden of additional cost - with larger organisations this doesn't hold up quite so well as with small businesses
Inability to organise work among staff - again most employers have a contingency for prolonged absences or shift changes
Inability to recruit additional staff - same as the first point
Negative impact on quality, performance or customer demand - they'd have to explain why they'd come to this decision
Insufficient work at proposed times - this is usually for people requesting amended hours not reduced hours
And planned structural changes - unless he's expecting to go into a more senior role that requires full time presenteeism then this is not likely to be an issue.
If they fail in due process or do not explain their reasonings, or their reasonings are unsatisfactory he can take them to an employment tribunal with the application being made 3 months less 1 day from the incident.
Like many parent carers though, he needs to consider whether his job is compatible with his responsibilities too, and that includes to you as well as the children.
You also need to consider if he's remaining in this position as it gives him financial power and authority over you as that is financial abuse.