I can't answer for the bed wetting since you say there is a history and it's hereditary.
But, without making a big deal out of it, I would certainly get a calender and document all the times he brings the kids home early or doesn't keep them overnight when he should, etc. You will be glad you kept track if he ever takes you back to court for more custody or claims he is the more stable parent.
I don't know how long you and your ex have been divorced or separated, but I'm sure it's not easy for your daughter to accept another woman in his life, especially if she feels he is choosing the girlfriend over her. Those are wounds that will be hard to heal and he will one day have to take responsibility for her feelings. I don't want any hate mail, but I personally think that people who dive into other relationships to the extent it affects their children in a negative way are being selfish. Him not keeping up with his visitation schedule for the sake of his new dating life is affecting his daughter whether he will ever see it that way or not.
Don't badmouth him, but don't make excuses for him either. Your daughter is old enough to convey her feelings.
This will be tough on all of you. Hang in there and document everything. I'm not one for court battles, Lord knows my ex has dragged me through enough, but if he isn't seeing the kids as he should, he is also violating court orders as far as his periods of responsibility and you could always say the visitation needs to be legally scaled back to keep your children from feeling hurt when he doesn't have them as he should according to the current orders.
This is all new so like I said, just keep a calendar and hopefully he will come around and see the importance of maintaining a close relationship with his kids.
Best wishes!