Almost every full child care center does school aged kids. They may open as early as 5am and close as late as midnight. I was open from 5:30am until 2am. I worked from about 7:15am to about 6pm every day. I drove the kids to school and picked them up after school let out.
Most child care centers charge by the week and it doesn't matter if the kids come 3 days per week or 5 days per week. That child is taking a spot in the classroom whether they choose to come that day or not. In Oklahoma, when a parent gets financial assistance to pay all or part of their child care expenses they pay the provider payments for that child.
For school age kids they pay about $11 per day, that covers their transportation to and from school, breakfast, and after school snack. During the school year they pay them more per day since they're eating lunch too plus staying more hours.
So you should be fine no matter what if you find a center that takes school age kids and transports them to your school. That can be the challenge though. Often I would tell people to sit in the parking lot of the school and make a note of which child care center vans drove through and picked up kids. That way you have the list of which ones to call first.
If you think about it almost all kids are in child care for over 10 hours minimum per day.
Mom has to be at work by 8, in her seat ready to go, so she needs to be there by 7:45am. She drops off kiddo by 7:15 so she can fight traffic. Then she goes to work for 4 hours until noon, takes an hour lunch and comes back to work another 4 hours. It's 5pm and she's trying to get out of the building but the boss comes up and needs to chat a minute, a co-worker needs her to show them how to do something, the elevator is full 3 times and she can't get on, the parking lot is chaos.......
So her day is a bit over 9 1/2 hours every day without anything going over. If she does get caught by the boss or the phone rings or something comes up then she's even later. So it's very easy for a child that has a parent working full time to be in child care at least 10 hours every day and truly most of the time they get dropped off around that 7:15 mark and are not picked up until almost 6pm.
The day costs the same no matter what so why not stop in really quickly to pick up a rotisserie chicken at Walmart or some other dinner thing somewhere. Most kids are in child care from just after 7am until almost 6pm daily.