No, not always. If the cheating spouse exposes the kids to strangers they sleep with that can prevent them having primary custody. And courts donot split debt 50/50 always, especialyy when it is deliberately done to financially attempt to hurt the other spouse. Judges do get p1ssed off about that behavior.
Oh, how I wish that had been true when it was my child exposed to the revolving door.
I wish what you wrote in the second sentence were true, but it isn’t, at least not in my state, according to every lawyer I spoke with.
As for splitting the debt, there are a few exceptions to the rule, as you pointed out. Another exception is if the spouse went into debt spending money on adultery. It’s difficult to prove, though.