Lisa -- the basketball game might last only an hour, but there's getting ready time, showing up early so the youngsters can put on their uniforms, and the aftermath -- showers, getting back into street clothes. Well....there goes the afternoon.
As I stated previously, I'd prefer that games be held on Saturdays or perhaps even Friday evenings. Some sporting events begin even earlier than 10 AM, making it even more difficult on a Sunday. Because of the number of teams on many leagues, playing runs into Sundays. Going to Church is something that is squeezed in rather than a focal point of the day. It takes careful management to avoid being rushed. Playing on Sundays per se isn't wrong with the proper perspective. It's getting away from the routine of the week -- the kids sitting at their desks, stationary much of the time. It's all of the other stuff that goes with it. Good conduct and sportsmanship should be an integral part of the game, no matter when it is played.
As far as your son is concerned, it would be helpful to plan some activity with him (trip to a zoo, park, museum or visiting relatives or many other possibilities) that accomplish the same thing -- a refreshing break from the school routine. It would help if he would find something to develop as a hobby so that he can devote time to it on his own without pressuring your time. It might be easier said than done, but he will need some type of outside interest sooner or later. There are so many constructive hobbies that he can handle on his own so there should be something out there to pique his interest. He just needs to discover what his interests are besides electronics and TV. Not everyone enjoys reading (both children and adults alike) but hobbies can be very absorbing and restful.
Ray, it's too easy to imagine alternatives when one also gets to make assumptions. Kids aren't pro athletes with uniforms and showers. For most sports, you get a tee-shirt. My own experience was one of very limited financial resources as were my parish and fellow parishioners. Sure, some sports are on Sundays, like track and youth football, but we are only talking about maybe 6 Sundays a year per sport.
I've been flying solo since my sons were 18 mos and 4 yo. I had the no TV rule and I did not allow video games in my house. Both my sons took lots of music lessons and played several instruments. We lived a half block from school and church, so transportation or teammates were never an issue. The boys on our street, fellow alter servers, could field a LL team and often did. The sports never interfered with our Mass attendance or Faith Formation. We were blessed with very devote Catholic coaches who led by example. It helped to have 3 and 4 generations in the neighborhood, too. Often, grandfathers would coach and they have so much more time to give to the development of young people's character and spiritual development.