If she is constantly asking your boyfriend for a "Just them night" I think she thinks she is in some kind of non-relationship with him. I would be 100% uncomfortable if my boyfriends female friend was always asking that, and if he planned a visit to her home, have a night out alone for dinner with her and then out for drinks. I would also feel embarrassed about it (Explaining his plans with others, or if anyone I knew ran into him on his 'date' night).
He has a girlfriend now, so any dates with other women should include you. She should be respectful of that too. But it seems like she wants him all to herself, is excluding you and is wanting to date him dispite him now being in a relationship. She is being unreasonable with him and he is being unreasonable with you by saying "Get over it". He is ignoring your feelings about it. But how would he feel if you did this say with a male work collegue?
My reaction to this situation would be exactly like yours. And, it would be a deal breaker for me if he went. I would tell my boyfriend it's not acceptable behaviour for him to drink and dine out alone with other women, even if it's making a date in the name of friendship. If he couldn't understand this, or wouldn't respect my feelings about it, I would realise that he's probably not going to be right for me. Relationships are difficult enough, you don't need another women in the mix. Eeek!
Hope this information helps! This is an interesting topic and I intend to make a Hub relating to the subject.