Hi reznorwells1994 :Welcome. Sorry to hear your mom has BPD/BPD traits. A professional would have to make an official diagnosis. It really doesn't matter if someone has enough traits to wear the BPD label. Just having a few strong BPD traits can make them a very difficult person to deal with.
Is your father in the picture? How old are the twins?
Is the vacation geared towards something fun for the twins? How have vacations with her gone in the past? Unfortunately, vacations are a common event where people with BPD traits go off the rails and make a trip miserable for others. So, if she tends to hold a grudge and wants to make you miserable, you might consider that in making your decision.
Do I apologize and lose face, or let the trip be cancelled and explain to my children that Grandma is sick?
What's the situation around the party and her not being there? Did she have an opportunity to celebrate with the twins?
Perhaps you can deal with this by validating her feelings.
i.e. I'm so sorry you felt left out of the twins birthday party. I can understand that you are upset. Can we put this behind us?