Oof. This is an uncomfortable situation and I'm afraid there's no easy answer. But the fact of the matter is that by refusing to interact with your dad's new wife, your mother will always be placing a huge burden on those around her, in an attempt to make herself more comfortable.
As your family continues to grow and evolve and more milestones are reached, that refusal is only to get more and more draining on you. Are you going to have to schedule two of every birthday party? Play calendar chess for each of your daughter's school performances from now until eternity? Eventually your mother will have to concede or remove herself from situations. She can't have it both ways. And I say this not without a great amount of sympathy for the hurt and frustration she must be feeling. Divorce is hard on everyone and this is in no way a demand that she should just, like, get over it already, but we've all got to make allowances and it sounds like you have been making a ton.
This will be a very hard conversation, and you don't have to come out swinging or with a major proclamation that she GET USED TO IT, but that you ask her to meet you and everyone else in the family halfway. She doesn't have to become best buds with this woman, but she needs to either be in the same room with her or get used to the idea of missing out on things.
Best of luck and congrats on the new baby girl!