I don't think, if he's Captain, he would realistically be able to do alternate Sundays. That's not how team sports work!
I feel your pain, however, as this was exactly the situation we were in. Worse, actually, because DH played on Saturday and Sunday when we first met! It was OK initially, as I used to go along and watch - helped by the fact that one of my friend's DP was also in the team, so we sat and chatted together.
But once DS1 came along it was very different, and being stuck at home without the car was a real issue. And it's hard trying to entertain a toddler for hours by the side of a pitch. Thankfully DH also realised it was an issue and that was when he gave up playing.
Is there anyway you could afford a second car - just a cheap run around so he can use that to get to his Sunday game? That was the only solution I could see at the time, had he not given up - because ultimately I didn't want to have to try and stop him doing something that he enjoyed and, frankly, was also good for him (both mentally and physically).
So, I think YABU to try and stop him, but he's BU if he doesn't understand your POV and try to come up with a way to make it work for both of you.
What's his suggestion?