Yikes, he does sound unhinged. I wouldn't blame the mother too much, she was getting inaccurate info about this "relationship". I couldn't help but chuckle though and wonder, if the woman was smart enough to see through him and know that the word "relationship" didn't mean what he thought it meant, and told him to "break up with her" because she knew he wouldn't listen if she tried to explain otherwise.
But yes, what the others said and in fact I'd suggest that you not go anywhere alone while at this bar. If you go out for a smoke, bring someone with you. Safety in numbers. Even if the guy never lays a hand on you, OP, it helps to have someone there so he can't say later "I never said that!"