Basketball wins. Unfortunately, sports will always win out. To be fair, there seems to be a communication breakdown somewhere along the line, but once games are scheduled opposing schools are notified and their schedules are also set. So to undo the game would affect not only your school's team, but another school as well.
You said you reserved the gym by going through the proper channels, but it seems that the left hand doesn't know what the right hand is doing.
In our school system, the athletic diretor is in charge of ALL scheduling - gyms, auditorium, all fund-raisers have to go through him so there's not too many or the same thing at one time. It really helps to have one person in charge of all the facilities and what is going on outside of classroom stuff and to be able to have a master calendar of every single thing happening in the district's facilities.
Yes, the PTO is a school (affiliated)organization, but the sports are directly part of the school. I don't like it anymore than you do, and being the type of person I am, I'd just reschedule with a BIG note about WHY you have to reschedule (in a nie way, but getting the point across
). Can you talk to whomever the people are who reserve the gym spaces and see whether they are coordinating with each other or where the problem stems from? I'd say at this point the only thing you can do is help it from happening again.
I'm sorry to hear about your situation.