OP, DS is on the spectrum. It's so, so hard. I get it. I honestly do. School can provide respite when he's being a nightmare (though tbh, he is mostly a nightmare when he's come home, because school is too much for him and he masks and bottles...)
The thing is, their priority and focus is DS, not you. When you feel desperate, you can't take any more and you need every scrap of energy just to stay a moderately adequate parent, the thought more may be asked of you is simply too much. I know. I get it. I call my mother and I am so, so lucky I can (sibling on the spectrum means she understands). But the school don't know you are not coping. All they know is that easing an ASD child, when anxiety is such a huge issue, into school is the way that seems, to them, most likely to make his school years a success in the longer term.
Forget SIL. To someone with a normal life and a normal frame of reference as regards time, 6 months is nothing. When you have a challenging ASD child and little respite, it can feel like a lifetime. Some days, till bedtime does to me.
So, practicalities. You need respite. You and DS both need you to have respite.
Homestart. Call them. You can self-refer, and you can access help asap. Practical, hands on, every week support.
Mencap's links page for autism can link you up to support groups. Other parents in these shoes can be an amazing support - your SIL can't begin to get it, but they live it too.
There is this charity in the Bristol/Cotswolds area which offers very good, sensory, expert respite care for ASD kids. They may know of one similar local to you. Call the National Autistic Society. Explain. Be honest. Ask them to recommend something, and tell them how on the edge you are. Tell them you need more support so you can support DS. None of us are limitless pools of emotional or physical energy.
Sleep. Does he? If not, are you referred to a sleep clinic? Has melatonin been discussed? Lack of sleep is soul destroying even if your child is otherwise easy.
DLA/Carers. Kids on the spectrum cost an absolute fortune, especially if they have sensory issues (DS can currently only wear Polarn oPyret and Frugi clothing - the rest are irritating. Shoes are an issue, too. He has to get his hair cut at one specfic place. If goes on...) If DS takes up that much time and energy, go to the Cerebra website and apply, if you haven't already.
It will get better. You have help out there. You deserve it.