I agree about him treating her badly, although we have yet to hear specifics from OP. Not that I don't believe her, but the changing stories and mudslinging don't indicate the most reliable of narrators. And we're talking about MIL staying overnight here, not just visiting. Personally I'd be grateful for her help and be keen to have her onboard, but she may well be a nightmare IRL and many people have a blind spot with their own parents who can do no wrong, while the in-laws are a combination of Saddam Hussain and Adolf Hitler reincarnated.
But as he cares for a 1 year old full time, I can't see how he can do what he wants all day, unless all he wants to do is to constantly feed, nappy change, play with, comfort, bath and nap a 1 year old. That on its own is pretty full on, and that's without school runs and part time work. If that's his thing, then maybe he is getting a great deal, but from experience, its a true fucking graft.
We don't know what level his job is, and "get a full time job" isn't the easy answer it sounds. Unless he earns at least 35k from it, they are probably better off with one of them being a full time SAHP, given that 1 childcare place alone, without the wraparound for the older two might exceed £18k p.a. If he can earn a significant wage, and they would be better off financially as a result of him working, their is perhaps a conversation to be had here. To what extent is it better for him to look after the baby and children rather than using childcare? Where is the financial crossover? What is his motivation? Its all things to discuss for OP and her husband.
But to dismiss him as lazy, and that he should get a job without knowing the exact details of the conversations and motivations is unfair to him.