Ok - so, if you want to keep the house, obviously you don't want to move out. It's a bummer about the in-laws, that they will have to move somewhere with your H, but you will have enough on your plate as it is. And it's possible that facing the reality (moving out and taking his parents with him) will make him re-think his "fun" little affair.

I think you're smart to get legal advice first. Also, you may want to accumulate incontrovertible proof of his affair, just so he can't gaslight you when the time comes.