I have talked to a lot of people who are divorced with children and all of the children have issues, even one of her friends who married someone with a child deals with the child having eating disorders and self-mutilation. I do not point any of this out though. She seems oblivious to these situations or thinks it will be different.
She also says she feels everything is a competition with me. That I am competing with her, and have to be better than her. This completely confuses me. I am not intending to compete with her on anything. We do a lot of the same activities but I do not bring up these things. She feels I compete with her for the children. I am not doing that. Playing with my kids is one of my brightest spots of the day. I get lost and have fun with them and it is the only time I feel unconditional love.
Don't concentrate on the kid aspect of it. You don't want her to come back to you out of guilt. And besides the one thing those other kids didn't have that yours do is... you. Be the best parent you can be. You need to show them that no matter what else is going on in your life you are going to be there for them. You're the father and they count on you. And definitely don't let your W hold you back from being a good parent.