Op is it possible for one of you to go full time and one take a sabbatical until things are more settled.
From seeing my dsis struggle against exactly the same situation (I posted further up your thread) I know there is no easy solution. Residential SEN school is the only possible solution for my nephew. Nearest one is 30 miles away, waiting for a place and have been for 18 months. He's done mainstream, mainstream with support, PRU, SEN school fulltime, SEN part time. Non work, he either gets excluded or refuses to go. The last SEN school was so far removed from what he needed dsis walked out after 10 mins. Said it would have been a masive safe guarding risk for the other dcs (mainly severely physically disabled, much younger than nephew). Fortunately the head agreed after watching nephew have a meltdown in the car park and attacking dsis car.
It's wrong, it's unfair, it's illegal. But the reality is there are very few schools that can cope with the type of needs your ds and my nephew have. Nephew is high functioning autism with PAD and ADHD. Plus dyslexia and some other learning difficulties.
He's also a big, strapping 11 year old now. Incredibly strong and fit, has absolutely no fear, climbs like a monkey and is frightened of no one.
At his PRU placement he escaped from the secure, padded room they had put in for him by going through a ceiling hatch. Then got onto the roof of the building. It took the police and fire service to get him down. My dsis is about 2 stone lighter than him, lives alone with him and is absolutely on her knees with it all. She phones the police (as advised by the mental health crisis team) at least once a week to come and help her when he's smashing the house up. Her car is usually undriveable because he's either smashed the wing mirrors off or put the windscreen through. Her house is more holes than wall. She has no internal doors left. The council have stopped replacing her windows and offered security shutters instead.
SS don't want to know. The LEA don't want to know. CAHMs don't want to know. The police are the only ones who have offered some support and have said that they will take him, then the only thing she can do is refuse to collect him which will mean he will become SS problem to solve. But no foster family could cope with him and he will just walk out of residential foster homes. The only hope she has is a secure boarding SEN place which are like rocking horse shit.
It won't be a solveable problem for you in the short term. Take some time off sick, assess your options realistically and then decide what you want, what's available abd what is possible. It might get worse beforw it gets better.
Dsis is 3 years post diagnosis of autism, 2 years since the PAD and ADHD diagnoses. He's had serious issues since he was 4. Even once he's an adult she will be his carer. It won't stop once he is 18.