I'm Lucy, and I'd be happy to answer your questions today.
If you have split custody, chances are that your child support payments are lower than what they would be if you had 100% custody. You may want to look at the state's calculator to get an idea what you should be receiving, because that can help you determine whether it's worth going back to court.
It could be easier for you to get a passport for your daughter if you had sole legal custody, if that's an issue for you. She only needs parental consent to get it until she turns 16, though, so it'll be moot in a few months (and doesn't matter if she already has one).
Otherwise, the primary protection in having the order changed is to avoid a situation where tries to have you held in contempt of court for not forcing your daughter to go to his house. You're really in the best position to determine if he's likely to do that. The most common reason a conflict would arise down the road is if one of you enters a serious relationship with a new partner (either because he wants to show his new partner what a great father he is, or because he resents you seeing someone new). Note that if you have anything in writing where you discuss the changes, including emails or text messages, you're protected. But, with the order as it is, he could come and pick up your daughter over your objection (assuming she'd go), and there's nothing you can do about it as long as the order lets him see her during that time.
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