Hi there,
Sorry to hear of the difficulties with your stepdaughter's mom.
Obviously, always act in the best interest of this child.
I strongly suggest that you and your soon-to-be-husband read a book called, "Divorce Poison" by Richard Warshak. It'll give you some proactive steps to take with this situation.
Your marriage constitutes a "
significant change in circumstances" compared to the conditions present when the original custody order was made. If dad has truly been "amazing," you probably won't have much difficulty get court orders for overnights to begin... and that's likely without the judge talking to the girl.
Also, after the stress and commotion of the wedding dies down, do consult with an attorney in your area. Unless dad has a huge skeleton in his closet (e.g., drug/alcohol abuse, molestation, etc), it sounds like amending the custody arrangement could be very beneficial for his daughter.
Attorney would have best advice on approach and timing.
Best,
DD