Uh, rewind a minute. What exactly about having severe anxiety equates to spooning with another guy? O_o
Anyway, I can see where your girlfriend is coming from, and with anxiety this situation will feel like a minefield for her. She'll need your help and support, and you may need to come up with a whole game plan in advance in order for her to feel she can cope, but I agree with you. I think it's important for building bridges with your family that she does her best here and tries to come along. Hopefully she has some coping mechanisms which help her get by in everyday life, and she'll be able to utilise some of those strategies in this situation. Talk it through with her, let her know how important it is to you, and ask her what you can do to make her more comfortable with the situation (you never know which small details might make it more manageable for her). She will probably find the process exhausting even if it goes well, so don't expect too much from her and listen if she lets you know she needs to leave/get away. If you can be by her side with this then she should be able to manage it, and ultimately it will be for the better as she'll be able to build a relationship with your family again. If you're both taking the relationship seriously she can't avoid it forever and I don't think she should reject the olive branch.
As far as your family are concerned, if they're genuinely willing to move forward then they must communicate this in their behaviour towards her. They need to be prepared to treat her with respect and make it a friendly environment, not just to tolerate her presence. That would be uncomfortable for anyone, and could be a huge trigger for her. If they are truly willing to move on from it all (which they should be if they respect your ability to make your own decisions) then hopefully your girlfriend will be able to relax into the day. As long as everyone's on the same page going in, you'll all survive to tell the tale.
Edit: If she flat out refuses to discuss it or go, then I think it sounds like she's using her anxiety as a crutch and that's not fair on your OR beneficial for her at all. And tbh, saying spooning another guy had anything to do with having an anxiety disorder seems pretty off to me (speaking as someone with severe anxiety myself). But hey ho, I've tried to give the benefit of the doubt here.