Hmm...can't really help here as I've been in the same position but am out the other side now contemplating how I'm going to juggle solo 3 kids in sport in the next yr or 2..arghh.
My youngest DS used to also nap at 3pmish...but I would only let him sleep for 30 mins or so or it would mess up his night sleep. Actually my DS1 was exactly the same, I would have to wake him for kindy run.
I used to do dinner prep in the morningidday when the toddler was relatively happy playing or "helping". Meals were extremely simple but healthy in those yrs...ie I'd make a salad early then quickly cook some fish/steak/chicken to go with it. Or chuck a pre-made lasagne or pasta bake in the oven while doing the homework/bath business.
Often I'll drop one kiddo, run home, cook dinner, feed and bath younger ones, do pick up in PJ'S and home for bed.
It's exhausting but I'm glad my kids do lots of sport. It's keeping my teen busy while lots of kids are just hanging out in front of a screen.