Your liability for debts can vary from one jurisdiction to another. Where I am, even if you are married you are only liable for debts in your own name or where you are joint signers. It does indeed vary widely. Ownership and definition of marital assets also varies.
Projection is a common thing that a "wayward" spouse will do - projecting their own behaviours on the other partner. Since she is (possibly) having an affair she assumes you are too. I would think that even if she isn't actively doing that she is a high risk for it.
The first thing you need to decide is what is it that you want. You have yourself and your two girl to consider. One obligation that you have as the LBS is to be the "sane parent" especially if the other parent is off dancing with the fairies.
You have some complex issues going on with both yourself and especially your W since she has a known mental condition which requires medications to treat. I hate to say it but on the surface and with the limited information I can see, your situation is unlikely to dramatically turn around in the short term.
So - presuming that you are heading for divorce there are a variety of things you need to do to "get your ducks in a row". Document financial things. Get credit reports done. Take an inventory of household goods (I just went around with a camera and took pictures of everything including serial numbers). Consult with a lawyer or two to understand the process in your region. Many will give you a free consult. Assuming you will be going for custody document when your W fails in her parenting responsibility. And most importantly, even more than keeping DR to yourself, keep all of this very very quiet. My ex went ballistic when she found out how prepared I was.
One important but cold hearted fact to consider is that at the end of 2018 the tax laws around spousal support will be changing in the US so if you are going to move, you would probably want to have an agreement in place before then.
Good luck. Keep your arms and legs inside the ride at all times. It may get bumpy.
On BD H52, W50 T27, M26 S21, D23 BD-9-Mar-16 D-15-Jan-18 Final-19-Apr-18 I am a storyteller. The story may do you no good. But a story is never for the listener. It is always for the one who tells