I disagree that it’s rude for them to talk about their interests when you’re out as a group of three. If it were a larger group of people, or you were all going out for the first time together, then yes the conversation should be general and inclusive. But at a certain point you have to let friends be themselves and talk to each other naturally. My husband has many friends that he will talk endlessly with, about music and food and other topics that don’t interest me that much. It doesn’t bother me because I’m free not to go out with him when he meets up with these people, and honestly he would say as much if I were to bring it up.
I can see why it’s weird that you were the one who met this person first, but that said, you were never very close with this person, she was more a casual friend. The friendship could have just as well died out naturally, instead your fiance has a new friend who you get along with too.
So yeah, I think letting them go out on their own is the best way to go, and you may have more fun when you do join them if you give them a chance to get their shared-interest chatter out of the way.