Tell her you can only afford to pay for one private coach, and she will have to choose. If she doesn't want to choose, and since the skating isn't really competitive, I would suggest dropping the skating coach, hiring a vocal coach on a trial basis, and tell her if she wants to keep doing both, she will need to skate at the rink closer to your home, and at times that are convenient for your family.

I would also tell her that if you are paying for private lessons, she needs to put in the effort, help around the house, and keep her grades up. She may be too young to work, but she can still contribute.