Ouch, this sounds like such an ugly situation. You have my sympathy. Until the cuz has actually broken a law, I don't think the police can get involved. If he's made clear threats against you or your children, then perhaps you can get a restraining order.
As far as him calling you names, just shrug, post a response, "Yes, I'm a b**ch, and will not have you taking advantage of me." It really doesn't matter what you or anybody else 'thinks" so much as you understanding what your legitimate needs are, and working toward getting those met. Having your own space in which to live and work is an entirely legitimate need. If I were a young mother, I wouldn't want to leave my children in a home where there's an unwanted 35-year-old man hanging out all day.
Stand firm, with both husband and his cuz, and try not to act too alarmed at the hints of malice, unless the cuz has a history of harming people. He could just hope to scare you into supporting him longer.
Good luck. I hope you'll post an update as the situation changes.