It is not right but you have no control of her. Acknowledge her pain that the birthday was missed by her mother and then do your best to celebrate with her! Make it an extra special one! Every birthday is so special and should be celebrated!
We cannot try to figure the mind of an alcoholic because we are not the A.
So many times I would try to apply logic or reason to my separated AH's behavior and truth is...there is just no rationale for the bad behavior. I've gone nuts trying to figure him out and in the end, I never will. Unfortunately, we are the ones left to deal with the immediate pain they cause, especially to their children.