Get financial and legal advice. And see a mortgage advisor.
Take with you all information on savings, pensions, policies, earnings, mortgage etc with you. This week is a good time to assemble all of that info from statements kicking around the house. (Unless it's all on apps on his phone and you don't know the details but lawyers can find it).
He wants his cake and eat it. It could be that she uses him for his money and then dumps him and he comes crawling back, but could you ever trust the man again? Nope.
So you have no choice really, he has to go. Up to you to decide what's best for the kids especially a special needs kid.
Some people get a flat that the take turns to stay in while the other one stays in the family home with dc when it's their turn to provide care, in order to keep stability in the family home.
Others just split and get new places or one buys the other out.
Living in the same house won't work for long so I wouldn't do that. At some point his girlfriend will want him to herself and start nagging him to move out so that's never going to be the permanent arrangement he hopes for an easy life with two women caring for him.
My moneys on him thinking with his dick. Mid life crises right enough. But very hurtful and life changing for all concerned. The price of his shag. Sorry you're going through this OP.