If you didn't admit any wrongdoing in regards to neglect of the kids then I wouldn't worry about it being introduced. Judges aren't concerned with whats going on between spouses, just whats best for the kids and BOTH parents being involved is usually in the best interest of the kids except is some severe cases IMO
What I admitted to is something I think would be minimized by a L in court. I grabbed my son's leg when he was punching his sister. It didn't leave a mark, no police calls or anything.
The way I apologized was completely over the top and, well, if I have to face that demon, so be it.
When I was about to move out, my W claims I left the house without telling her while I was watching the kids. I did tell her, and at the time she was with all 3 kids, but she didn't hear me. She treated it like I was dangerous, like I might be watching the kids alone and just walk out of the house. (!) It was a minor thing. That is probably the other incident she would raise.
Right now we are in a roughly 28-72 custody split. I'd like to be 50-50 in a year ideally. I think there is a very clear way to morph our current schedule (4-10) into a 2-2-5-5 which would work quite well -- of course I doubt my W shares this view!