As a child of a divorce that went on for 10 years, be done with it. It's causing drama and tension. I can understand wanting to keep something you've been paying on, but letting it go will be best for you and your family. Offer her one for herself if she'll take her name off both, her choice. If she refuses, tell her you will take it to court. If that doesn't sway her, then actually do it. Do this all through email or some other written form.
Don't let this go on for the sake of you and your wife and even your ex. Even though you are providing her with free vacations, you could do that without this entanglement that is causing tension. Unless this is about your feeling entitled to it, this is truly best for her too. Life is way too short.