So I'd like to start off by saying that this is an issue that I have had with this girl before I started dating my boyfriend. To keep a long story short, she rushed my sorority twice and did not receive an invitation to join, and because I was an officer in the organization at the time, she blames me for not getting in. Her and her mom like to call me a "swamp monster" behind my back because she like to gossip to her (apparently about my appearance), and she is overall the spoiled, beauty pageant cheerleader type who throws a fit when she doesn't get what she wants. So right off the bat we obviously don't have a great relationship.
I have been dating my boyfriend for 2 months now, and things are very good between us. Sometimes we struggle a bit with his communication (sometimes he says stuff we good intentions that come off as hurtful, but I always make sure to tell him when he does this so he understands and so we can work on it as a couple.) I feel like he is my person, we complement each other very well and have very similar personalities and views on life (I'm an INFJ if anyone wants to know haha.) Overall, the relationship is great and I am very happy with how things are.
This is the only major issue I have had since we started dating. From the get-go, she made it well known to people within our mutual friend group that she didn't like the fact that we were dating. She has told people that he could do better, and I found out at one point that she was spreading rumors about me that I was telling my boyfriend he couldn't hangout with her or any other girls, along with other things. It was all false, so I talked to my boyfriend about it and explained how much it hurt my feelings that she was actively trying to spread rumors about me. He responded kindly that it was mean, but a little dismissive as well. When I told him she got in my face at a party, and I was going to hit her before someone stepped in between us, his comment was "please don't get into a fight with her, because it will make my life really awkward." I felt like he was just saying that because he didn't want to get caught in the middle of it, and wasn't thinking about my feelings very much. They are decently good friends. They had classes together, do projects together, and hangout in group settings a lot. She has known him longer than I have for reference. I feel like her presence creates tension in our relationship, and it just makes me feel really uncomfortable.
Since that happens, he often avoids telling me that he's hanging out with her, usually mentioning other people in the group but not her. The other day he went someone with her to look at a dog she wanted to adopt, and sent me pictures of the dog, and when I asked him in person why he went there, he struggled to get out that he had gone with her. I trust my boyfriend, he has never given me a reason not to trust him. I think what makes me so uncomfortable is that he spends a lot of time with someone who is very verbal about the fact that she doesn't like and has told people that she thinks we shouldn't be dating. She is just such a mean-spirited person, I really don't understand how he can't see that. She must be a very good actress.
Overall, I'm not sure how to handle the situation. Im very verbal about the fact that she isnt welcome at any of my sorority's functions or at my house in general because she has been so rude to me in the past, but at the same time I don't want to be the girlfriend who blocks her boyfriend from seeing people (I don't want to be the girl she claims I am.) I just don't know how to tell him that him spending so much time with her really bothers me. What should I do?