Sigh...... Story time. I have two "kids" (adults, now).... A musician and an athlete (field hockey), although both played baseball & soccer as youngsters. Problem was, their other parent lived 300+ miles away, so got one w/e per month and the entire summer (minus two - nonconsecutive - weeks for me). That pretty well killed summer sports for them. Scouts were a problem, too, due to summer camping, etc. But, ya know? Their time with their other parent was, in MY mind, in their greater interests than time with coaches, friends, Scout leaders, etc. Music was easy to work around, field hockey less so. And funny..... Dad wasn't too willing to give up his limited time. And not only did *I* understand that, I worked with the coaches, etc., as best as possible, so that they also "got it". As well as explaining things to kiddos.
Honestly? You need to figure out the carrots to offer to Mom. You'll p/u kiddo and bring her back, and offer Mom extra time - school breaks, summer time, etc. to make it work for kiddo - as well as pay all associated costs (club/team fees, uniforms, shoes, gloves, travel expenses, etc.) - be aware it only gets more expensive as they grow. If she's decent? It will pay off. LOL Kind of. Mine got a full ride to college - oh, except housing, food, books, etc. Sports - like any extracurricular - are not cheap. And don't be shocked if she gets burned out by high school - a lot of kids do.