The fact that you have your child 50/50 is an awesome thing.
As far as her saying she wants someone else, or she hates you...it only gets worse as they get older. If my daughter gets mad at me and says she wants her daddy...blah, blah, blah, I say "Good, that means I am doing my job". Of course when her daddy pisses her off she says she wants her mommy. So she probably does the same thing to your ex. That is just a kid thing.
Like I said, if you think your ex will be a bitch about it...don't give her the satisfaction. Be the better person, and your daughter will thank you for it later.
