Whereas in reality he's already left you. You're his parents carer now. You think he's staying home every evening by himself to save money so you can join him? No social life, hobbies or sex life for 6 months? I think that's doubtful.
Why wasn't all this information found out and discussed with you and agreed with you before he took the job? How much money does he need to save and how long will it take to save it? If he's needing enough money in the bank to fulfill government criteria to be able to support you all, that could be (tens? hundreds? of) thousands and take years. His plan doesn't sound realistic.
I'm wondering if the plan is actually he starts a new life abroad, you are now both his parents carer and basically a single parent. They die, he inherits the house and that's when there becomes enough money to move you to wherever he is now.
That way he avoids sorting out any care for his parents, his inheritance their home never ends up being sold to pay for that care and he avoids the demanding small-child years of parenthood with the effects that period tends to have on a relationship. Instead he can relax happy that his parents are cared for and he'll inherit, enjoy the single life now and still have his family (you and DC) there as backup plan for the future.
It's been 6 months, there appears to be no real plan. Formally separate, find yourself a job and a home to rent, claim whatever benefits you need to to survive and tell him you're not being his parents carer any more. Its time you had a life too.