How should I go about asking this?

Only thing you can do is ask. Just explain it to him like you explained it to us. There is no secret way of asking that will make him say yes. Just say please. And hope for the best. If he still says no maybe offer to go home straight after school then walk your dog then go out with your friends. My dad hassles me about walking my dog too. So after practice me and my friends usually go get my dog walk him then go hang out. So depending on how out of the way your house is that might work too. Goodluck.