Most moms that work don't have the luxury of paying an additional caregiver to go pick their child up from child care to take them to activities.
I suggest you simply tell the coach that you work until XXpm and little guy can't be there until I pick him up and get him there.
We just can't do it. IF you want to give the coach, or another parent, permission to pick up the little guy up from child care on the day he practices then that's an option.
Otherwise you can hire a nanny to take care of your child after school.
A nanny is contract labor you DO not have to pay SS or vacation or anything like that. You simply pay them by the hour and then you pay them more on the days out of school and if they do extra things like cook dinner or do loads of laundry or other stuff you pay them per load or by meal a set rate.
If you want to do a daily rate for after school care and a daily rate for out of school days you tell them in the interview this is what I pay each day and you are responsible for picking him up at school and taking him to any and all after school activities that are on the calendar. Gasoline and wear and tear on your vehicle is $XXX per month.
When we've hired a part time person this way we told them they were responsible for about 4 hours per day on school days and they'd be driving about 6-8 miles per day and this was how much we paid for that travel. They'd need to have a snack prepared for him when they picked him up and I'd supply the food.
Some days, in the off season, they'd simply pick the kiddo up from school and bring them home to hang out and have a snack.
It was straight forward and written down so it wasn't confusing.
It will cost more than after school care since you're paying gasoline and other chores like cooking a snack and a bit more time.
So all in all I'd try to get a parent or coach to just pick him up or rearrange his classes to where you can get him there.
We have some grandparents pick kids up from school and then drop kids off at class. Moms or dads pick them up when they're over. Talking to the teachers and just putting kiddo in later classes is actually the most cost effective and best option.