Have fun at the party. I personally don't think I could do it.
What's wrong with addressing what she wrote? She's hurting too from all this. She is also a victim of this betrayal. Or isn't she. Can't you say, "thanks for the birthday wishes, the support, and offers of support. I'm holding up well. I'm sorry if you felt snubbed, it wasn't intentional."
You could tell her that you do hold some resentment because you feel she had a role in encouraging your wife to leave. What's the harm in that? Maybe she will say she didn't tell her such things. But all of that is certainly up to you. I can't blame you for not wanting to be friends with her (is she cute?).
TTFN
Me
In the end, it's not the years in your life that count. It's the life in your years. Abraham Lincoln
It is hard to fail, but it is worse never to have tried to succeed. Theodore Roosevelt