I'm a little confused. Are you thinking of putting him in ps so he can play football, because he is lazy, because you have to constantly remind him about chores and homework, or a combination of all of this?
What do you hope ps will accomplish?
Will he be able to play football...probably.
Will he still be lazy, getting by with as little as possible....probably.
Will you still have to remind him about chores and homework....probably.
Can he not play football and still be hs? I don't know what your priorities are but with us home always comes first. You must be respectful, responsible, and take care of the home front before extra curricular activities are allowed.
It sounds more like you are at the end of your rope (we've all been there) and looking for a solution. Only you can decide if ps is the best option for you, your ds, and your famiy. But, imho, it won't solve the probelms you have mentioned and could actually make them worse. I have worked in the ps system and irresponsible, uninterested, rude, disrespectful students seems to be the norm.