Am I the arsehole for feeling like his mum who doesn't work should be caring for him rather than disrupting our life?
Yep. If it's all about disrupting your life. Absolutely.
She gets paid £3k, then £2k but then that £2k includes all benefits, including the disability ones and keeps the roof over her head?
She won't let her ex see his child but then again, she wants you to have him all the time? You don't have a disabled child. You have zero idea of the complexity of it, the sheer relentleness of it and everything else. And even less than zero idea of what it is to do it alone.
You have no space but insist on another child? Therefore the disabled child is the one who must be removed because of the disruption he brings to your life? really?
All that said, if she's not going to look after him, he needs to move in with his dad and his dad needs to claim the benefits. You will then need to decide if you are staying or not. It's not his ex's job, however, to care for a disabled child so that your life remains interruption-free. The child has two parents, both need to work out how to manage caring for him. If one is unable to do that, then the other has no choice but to step up and do it.