I don't think it helps to make anyone think they're being immature, even if they are. Everyone's feelings are important to them, no matter how immature they are. Her reaction may be immature, but her feelings are certainly valid, after all, she was the one in the relationship, she might feel something she hasn't told you, and you may not fully understand how she feels. If I were you, I would just give her time. That's all any break-up takes to overcome. I broke up with someone over 3 years ago, I have a boyfriend that I love more than anything, but still when I see my ex, I get really uncomfortable. At first I was just as immature about it as your cousin. It's only been recently that I can talk to him in a fairly human way. I wouldn't stress too much, I think these things have a way of working themselves out. Your cousin will get over it, especially because you're family; she knows you love her and you know she loves you. That's the most important thing to remember, but we can all admit that that fact gets a little cloudly sometimes. Just give her time to let it become clear again.
Very good points. She did say that my calling her "immature" and constnatly inviting this guy places shows my insensitivity to the issue. I thought she was ridiculous, but yeah, i've never been in that situation. Thanks.