It's one thing if your daughter really likes to run but your ex is really throwing up resistance because, well, who knows? Maybe because she knows you'd love it if your daughter ran sort of seriously and reckons you and your daughter will grow closer if she runs. That happened in my family with hockey. My nephew was a good youth player. His dad was totally into hockey, played in an adult league, and was at pretty much all of his son's hockey events. It was their best bonding thing. My sister made it as difficult as possible for this to happen after the divorce. Eventually my nephew gave up hockey completely, contact with his dad dropped way off with plenty of encouragement from my sister, and my nephew's life started on a serious downward spiral that lasted for maybe fifteen years.
If you think your ex is discouraging your daughter from running because it would make her closer to you, if you believe your wife is discouraging your daughter from running as a weapon against you and you're convinced your daughter really wants to run more seriously you should do what you can to make it possible for her to run more. Without knowing anything about specifics I don't have much in the line of suggestions as to how to make this happen.
On the other hand, if your daughter is really showing only casual interest in running at best, if the only reason she'd go out for cross country is because you want her to, I'd say to let her alone and do things that she wants to do. Even if she's not showing interest in running now that can change and if it doesn't that's fine. Find other ways to be close with her.
Both of my sons ran seriously in high school and college and still run seriously in their late twenties and early thirties. At twelve the younger one wanted no part of being a distance runner. I never pushed the sport with either of them. But they saw me run every day. They saw me come back from races showing occasional signs of satisfaction. I'm sure I influenced them but becoming runners was never a goal of mine. In your situation the decision to go out for cross country or not should be her decsion alone.