Grandma vs. Grandma

I'm being induced next week due to a complication and all family on my side and my boyfriends side is aware. They are all excited and can't wait to be up here asap. Only problem is the grandmas. My mom has never met his mom due to the fact that she doesn't like meeting anyone. She's been with the same man for 2 years, married him, and still hasn't met one single family member of his. It's just how she is, it's anxiety. But her anxiety with meeting people is causing her to be very rude towards my boyfriends mom. She told him last night that she better be the first one to know, first one to be here and the first one meet our baby. Her exact words I believe where "I'm more important than she is. That is my daughter the baby is coming out of. I will always mean more." My boyfriend said "but you guys are both the grandmas" and was very hurt and it takes a lot for him to get there. She doesn't care, she believes she will always be #1. I was fighting back the tears because I knew this is how she'd be. It's so frustrating and I don't need this extra stress. How am I supposed to say to his mom "sorry but you're not allowed to see your granddaughter until my mom has" ITS SO STUPID. I'm trying to focus on having a healthy baby since she'll be coming 5 weeks early but all I can think about is the potential disaster it's going to be when the grandmas meet. Why does family have to act this way at a time that is supposed to be so happy and bring everyone together?