Well, I'm never going to agree to her having sole custody. That's a deal breaker for me.
I doubt she'd ask for it. If you assume the best from her, but prepare for the worst, it might help. Remember, she might be afraid, too. One book I read suggested (I think accurately) that women fear most being isolated/alone/rejected. Even though this is her doing it, if she was saying on your 5th yr that she felt you would leave, she might be doing the D having convinced herself that you would have left and that her lack of effort was just saving resources. Like you said, she's surrounded by bad examples of a M.
Unless you are abusive or mentally unstable CTH, I don't think you have to worry that any judge will give her sole custody. If she argued that against you, it sounds that you have a good memory of enough events that you'll be fine. I've read custody is decided by who did what in the marriage, as well as who is doing what. You are spending time with them in ways that amount to more. I would only worry about proving you can uphold (after payments) an apt/house that is sufficient and stable for your girls - even better, more stable. There is some resarch that shows that girls particularily do poorly when the biological father is not around as a teenager. If I remember the research study link, I'll send it, otherwise, 4 hours of google found it for me.
Have you attempted what TulsaTime suggested...if you wanted to? W&I are separated in the same house with a D date in May if I/we can't figure it out (so far...improving). So if I decided to just move on and ignore her, focus on myself, I would've lost the opportunity to touch her and say I wanted to be with her. I'm not saying pursuing, just look for the opportunity to surprise her. If she was in an A, you were violent, you weren't trying to improve yourself, you were always flirting with others, then there might be no way. If not, there is always a possibility, no matter how small. But if you don't look for it, it could never be found.
My W's biggest concern was trying only to be rejected. I told her that if she didn't try, it only guaranteed rejection. It hurts to be kicked to the curb. I think it hurts more to think 'if only' - I keep harping because you've mentioned wanting her to change her mind so often, that I think you need to put that into action.
I'm not sure if I or others have mentioned it, but reading "Improve your marriage without talking about it" helped me understand my W's insane fear of rejection/desertation. Even if you don't want to try anymore, it might be worth it because I've tested it on my students, and I think it is true about elementary girls/boys, too.