Ohhh. I didn't realize that. In that case, I'd say that Dad really does sort of have a say in whether son goes or not. So I'd probably present it to the dad something like this:
Son really wants to go see this game and it is during the time he will be with you. If you want to take him, I'll spring for his ticket.
You might even suggest that they can certainly make it a family (as in Dad's family) event if they want since you mentioned your concern that it might take time away from them.
Alternatively, I agree that if the son is old enough to handle it, he should do the asking. And he can say that he really wants to go to the game and that you've offered to pay for his ticket if dad can take him.
Now, if dad says no, he can't go, then you can bring up your brother. But really, I can kind of sympathize with dad that if he can't go, he'd rather son didn't go either since it would seriously cut down on his time with dad.