All of these point to a lack of cooperation on all sides and your daughter is paying the price for your inability to get along. I have a lot of experience with this type of situation as the parent of a 6 year old and an 11 year old, but I find your attitude as bad as your ex-husband's. He has the control of the insurance, you have custody and your daughter has a health problem that won't get better until you do. So why don't you start by being willing to cede some control. I can understand why your ex is reluctant to put his daughter under the knife.
Doctors are in business to sell surgery.
Try to step back from the situation and see that you and your ex want the same thing. It may then be easier to share the task of deciding how to proceed. Your daughter will NOT love you more because you took control of the situation. She will love you if you find a way to get along and reduce the tension. If you act like a grown up perhaps your ex will follow the cue.