My ex's parents are mad at him, and he doesn't want me to bring her to see them?

You're a great mom i agree :) I think that you should perhaps talk to your ex's parents one more time and let them know what's going on. Have them work on the issues. Also you're the mom. You shouldn't back down and threaten a lawsuit because he's the father; you have more of a right to do what's best for your daughter. If he throws a fit, hang up the phone, kick him out, call the police or threaten to. You have to let him know who's boss. And I would keep letting his parents see her.