No one is a perfect spouse...no one. The important thing is whether or not you've treated your spouse with the same respect that you'd want yourself to be treated with. And FWIW, children learn about romantic relationships and their roles from the first ones they see....their parents'. By leaving, you've taught them what is acceptable and what isn't.
I don't know how you prove that you are providing nightly support other than witnesses or documentations of time spent out doing activities (i.e. receipts from taking them to the movies, whatever).
If you have any access to admissions of guilt like emails she has sent you or she has sent from a joint account to another (therefore there is no expectation of privacy), that would be good. Excessive phone calls and/or texts to other guys, especially a single one, that she has no professional relationship with would help (although that in and of itself isn't "proof" as arguments can be made for friendship). If she has had an affair with one guy and dropped him for another one, the first guy might be willing to testify against her....stuff like that. And, of course, pics of her seeing a guy in a romantic situation or spending the night at his house, would all help, but I gather that you don't have those.
By financial support, I mean that you are obligated to pay child support for the provision of your child's necessary living expenses. The amount is determined by gross income and altered by the amount of overnights spent at the various parent's houses. There is a calculator on this site that can help. FWIW, there is a big difference in amounts paid/received between 122 and 123 overnights. The more overnights a parent takes, the less he/she will have to pay if they are the supporting spouse. Part of this is to encourage parental involvement by both parents.
Any legal problems she is involved in post-separation are her own responsibility, although as far as the car company is concerned, you are responsible for any debt owed on the vehicle since you were the owner. That debt can be used in negotiations during the divorce to offset equitable distribution. FWIW, any criminal activity or DUIs that she is involved in can be used to establish as a pattern of irresponsible behaviour which may not look so good for her when it comes time to debate custody. A single one in and of itself not so much, but the DUI along with staying out partying too much, any other separate arrest events, or having a string of romantic partners in a short period of time will lead a judge to believe that maybe she needs to get her act together before resuming full-time parenthood. Judges do tend to look with favour on the parent who wants to keep the other parent actively involved in the children's lives though....as long as it isn't harmful to the children's emotional and physical well-being.