MIL is a whack job, but bear in mind too, you don't know what kind of nonsense H is telling her.
See an attorney and look into filing an order for temporary support. Make sure you are protected financially.
Your H is a recurring cheater and frankly, kinda out of his mind right now. He would have to do a LOT, LOT, LOT of work to become a person you should let back into your life again. Not impossible, but also, not super likely.
Focus on creating the best possible life for yourself and your kids. Focus on becoming the best YOU that you can be. If he happens to come back later, YOU can decide at that time whether you want him back or not (you might not!). But for right now, just protect yourself financially and move forward with enjoying your life. Pretend he's gone on a one-year ocean voyage, so you might as well have fun and focus on improving your own life.
