Just because he is staying with you don't give him any more privileges than anyone who would stay with you, whether that be long or short term. He is not paying board, he has two feet and two hands so he should be pulling his weight around the house like everyone.

I think you need to make a roster for both the boys and be very strict about it being kept. It sounds like your DS is a good kid but this way he will be on the same playing ground as your SS. If the chores are not done then there should be consequences and no swapping chores until the next roster is done.
At seventeen he is more than old enough to pull his weight and if he doesn't like the rules then he needs to decide where he wants to live.
Your DH is doing him or the rest of the family no favours by not making him accountable for his behaviour

I hope you all find a way to live together as a true family