Not a lawyer, but the money stuff will follow whatever legal rules there are. For the most part these days, property that you enter into a marriage with is yours after a divorce. If your father in law didn't write you a personal check, then at best, anything he gave you was part of the marriage, and would likely be split 50/50.
For now, I'd assume the money is not yours unless you put it there yourself. Get a lawyer ASAP. They can tell you the answers to these questions.
If you can change the access to the account that is in your name, talk to a lawyer but it might be a good idea to do that.
Whatever you do, don't spend anything that is questionable.
> Even though he's a wonderful guy and has always struck me as a guy of integrity
What happens with a breakup like this, is that people pick sides. If you go the route of telling your inlaws about the infidelity they might be more likely to treat you with compassion. If they think you're bailing out, they'll chose their daughter. By default, parents always choose their children. TBH, i'd tell them or at least intimate that she's been unfaithful. You don't need to give them details unless they ask, but it's part of the story and they should know it.
When i got divorced, someone sent me this book and it really helped. The next few years for you are going to be pretty tough, and this helped me a lot. https://www.amazon.com/Crazy-Time-Surviving-Divorce-Building/dp/0062337408/ref=dp_ob_title_bk