You need some time off, mama!
I can see his point - high school only lasts so long and then there are no more games (unless you've got college athlete potentials on your hands) and I don't think he should have to miss the games. He should start skipping some practices to stay home with you.
Have you thought about going with him to the games? I know it sounds daunting, and I can't imagine you would last through an entire game, but LO was always a better baby when we were out and about, and personally I could not stand being in the house all day. It was work to haul LO around to their soccer, basketball, scouts, etc., but he enjoyed watching the activity. Babies need to be in stimulating environments, too.
I would at least try it. It would show support to your stepkids and to your DH. You are a whole family, and you need to act like one.
Secondly, and as important, you need to work out time alone. Tell DH that you need a night or two off each week for you to go out and meet friends or whatever you want to do, without the babies.
Date nights with DH alone are great, too, but don't neglect yourself and deprive yourself of time by yourself.
Hope things get better! I miss the cute baby faces and all the snuggle time, etc, but I do not miss the work! As soon as LO turned 3 it was like I was a new woman again.