Problem with a friend

Hey there. Well I'm sure some of you will think this to be a bit of an immature thing to be asking problems about, but I genuinely think I am being the more mature one in the dispute with my friend. Tonight I'm meant to be going out for a meal with a few friends to celebrate my birthday (my 17th). For about 2 years, I was very good friends with this particular girl, and I was very good friends with the guy she liked, and when he rejected her when she made a pass at him, she told me she couldn't be my friend anymore, as I was friends with the guy. Well I wasn't going to fall out with one of my best mates, just because this girl wanted me to, and the guy never had any problem me being friends with her. So, that occured about 5 months ago, and since then I think we've spoken a total of about 5 times. We're not rude, it's just like we've moved on, if you get me. I'd still class her as a friend, but not a very close one (especially due to her past behaviour. Like I felt she would pick fights, like accuse me of something, that everyone else in the group didn't think occurred either. She kept causing me all this stress, and at that time, my grandad was in the last stages of cancer, and sadly died shortly after, and only then did she speak to me, to say she was sorry). So, intially, I wasn't going to invite her to this meal thing, mainly because she doesn't hang around with our group at all, and only speaks to me personally very occasionally. However, since I was invited to her party last weekend (which was a big party where everyone was invited, so it wasn't like I was specially invited) I decided I'd invite her along, and then it would cause less trouble, as she kicks up a fuss over nothing. She had askes me what I was doing for my birthday, I told her, then the conversation moved on, but before I left, I mentioned it to her, and she said "yeah", so on I thought she was coming. I however received a sarcastic message from her this morning, saying her invite must have got lost in the post, and it was a generally rude text message. I told her she had been invited, and told her when I had asked her, to see if it would jog her memory, but she says she remembers that conversation completely, and I said nothing of the sort. She also mentioned that the reason I didn't invite her was because we don't speak anymore, as told to her by a friend, who is both our friend, but seemingly I now know which side her bread is buttered, but even then, I 'll admit to her face that's what my initial thoughts were, because she did barely speak to me!!! She hasn't since, but I finished the message saying I didn't want to argue with her, and I wasn't going to beg her to come (which is probably what she wanted), and that the invitation still stood, if she wanted it. Kind of like a truce, and be the more mature one. Maybe I'm wrong. When I read that message this morning, I felt shocked and hurt, but now I'm actually in the mind frame of I don't care to be honest. If she's going to be like that, and say I didn't do something that I did, I don't think she's worth the hassle is she? What do you guys think? I'm sorry for the ramble, but I really would appreciate your thoughts ASAP. xxx