@thetwister No experience with this, not an expert or lawyer or anything.
I'd start by documenting any evidence of the affair that you can, with dates and times and everything. I'd imagine that during a divorce/custody/alimony process, this sort of documentation will be really helpful to your case. Especially if you're not in a rush to leave the marriage, getting some evidence together first seems like a good idea.
And then like others said, probably start discreetly looking for a lawyer and get some better, professional legal advice. As a SAHM, I imagine you'd be entitled to some sort of alimony, but that likely depends on where you live.
Secret bank account and secret part time job? (My mom is willing to watch the kids while I wfh- I have a job offer for 1,400 a month, and I can hide working).
I would personally think that opening your own bank account is a good idea. Start putting any money you can into it. Savings for the future, or to pay a lawyer, or whatever. It also sounds like your mom is supportive and has the ability to help a little, so I would definitely take her up on any support she can offer. But rather than jumping right to school/work, I'd maybe use this time to again, talk to a lawyer and get professional advice first. Perhaps your mom could also help you keep any sensitive legal documents or evidence against your husband at her house, and stuff like that?