jessica,
I really liked ocean's idea for a family meeting. Sounds like the elephant in the room needs to be addressed. You say he thinks making you mad is a game. That makes me think this is less about the actual dishes he's refusing to wash, and an indicator of a bigger problem. I mean, IF the only problem was that he doesn't like to do the dishes, I could see changing that out for him. Have him scrub the toilets instead. And plenty of men have scrubbed toilets in basic training, so no gender specific chore list is an argument for toilet scrubbing. In fact, every time my 12-yr-old says the "s" word, he earns the honor of scrubbing a toilet. Keeps our toilets and his mouth clean.
I suspect your
DH hasn't given an indication to his son that chores are important. If your DH doesn't really buy stock in the idea, it's doubtful that his son will either. Makes me wonder what your DH really thinks. Does he really believe you should be doing all of the chores? That could be key, finding out what he really believes. Not just what he's saying when under pressure.
Sherry had some good input as well. It doesn't sound like your DH is teaching his son to respect you. And that has a potential for big problems in the future, oddly enough with consequences that will be felt mostly by your
SS. Once he learns from an early age that it's okay to disrespect adults, to do what he wants and to balk at authority... guess what will happen when he gets pulled over for a speeding ticket. Guess what will happen the first time his boss reprimands him (and the 2nd time and 3rd time as he starts a career of job hopping when his boss pisses him off). You can imagine what sort of decisions he'll make when he doesn't worry about anyone but himself. He'll make unilateral decisions when he's married and wind up divorced. About the best thing that could happen to an unruly, disrespectful young adult is basic training. He'll need some training instructor in his face, retraining him that he's not the king of the hill, when his life could have been so much easier if his parents had taught him that from the beginning.
But you can't do it alone. And your DH won't do it under duress. He has to believe that he has valuable instruction for his son, which his son needs, to become an asset rather than a draw on society. Lessons that will help his son have a happy life instead of continual disappointment. Counseling may help in this regards between you and your DH.
As for the dishes, since your DH works to much, I'm guessing you do plenty for your SS. When my
SD lived with us, she relied on me for rides to the movies with her friends, trips to the mall, supervising her and her friends, doing her laundry, hosting her parties, feeding her friends, etc. I didn't look at our relationship so much as a stepmother to stepdaughter relationship. Basically, if she scratched my back, I scratched hers. When she stopped scratching, I followed suit. Didn't take her long to figure that out. Sounds like you're already doing that. But it also sounds like you may be allowing your emotions to get sucked in.
It takes two to play a game. Sounds like your SS wants to play. Do not get mad, and do not play.