Housemate has rls, takes mirapex, (pramipexole) but is obstinate, argumentative, stays up all night, refuses to get adequate sleep. How do I get him to get rest?

?mirapex (pramipexole) reaction? Unfortunately, you are describing a behavioral problem, but not clear as to whether this started before or after use of mirapex (pramipexole). Since the latter drug can cause a behavioral dyscontrol syndrome, need to discuss all of this with your doctor and make some decisions. If the drug is the culprit, other meds may work just as well for the rls, and not cause similar side effects.
Try counseling. You don't say if this is a roommate or an intimate relationship. If it's a roommate, sounds like either you or he needs to move out. If its an intimate relationship, it sounds like some discussion with his physician about his habits and temperament might be helpful. His doctor could perhaps refer you both to some couples counseling over these issues.
How to get some rest. I don't think you will be able to get him to get adequate rest on your own with any standard sleep aids such as tylenol (acetaminophen) pm or melatonin or even talking to him about it. He needs to discuss this problem with his doctor and if that is insufficient, if it is disrupting your household perhaps the 2 of you should seek counseling together on this matter. Good luck with this problem to both of you!