At this age he is fully able to be in charge of himself with his coaches supervision at practice. You stated that you can drive him there and then go back to get him so you routinely leave him in his coaches care.
I think that is acceptable. If she is picking him up from practice at 11 then that is when she is responsible for him. If she is taking him and bringing him home perhaps that would be different.
In child care she would only get a portion of what you are paying her. She would get about $11-$15 per day for him in Oklahoma if she was operating a child care business. That would include feeding him too.
I think what you are offering is fine. If he were younger and more needy then more per hour would be needed but at his age he is almost old enough to stay home alone. Over the next year he needs opportunities to learn how to manage simple tasks so he can start being responsible for himself, with you in the home he is more than safe even if he is heating up lunch on his own and entertaining himself.
What I would budget for this summer is what you said. Then by next summer I would chip in for gas and have her just give him a ride there and back to your home. No babysitting at all. Just giving him a ride. He can learn to let you work and you can teach him to be self reliant.