Your poor son. Watch the movie "As Good As it Gets" with Jack Nickelson. (Not with your son.) This is what your son has.
Talk to his pediatrician. He can find someone who works with this condition. There is also medication to help it. Can you imagine how stressful it is for him to have such a COMPULSION to have to wash his hands? Are his hands chapped and sore? I'll bet they are. That's miserable too.
Please, please stop quarreling with him. You don't even know what you're doing. You haven't tried to find out how to deal with this REAL problem. Yes, it causes pressure for you, but you and your husband are adults. He's a child. HE'S the one feeling the most pressure.
Get help. Get help for him NOW.