Dealing with Divorced Grandparents meeting their first grandchild

My mom and I went through a rough patch after the divorce -- she wanted her kids to take her side, we tried to stay neutral, she took it out mostly on me (the oldest) and didn't speak to me for a few years (with the exception of some very mean words every now and then). She didn't go to my wedding last year, didn't even RSVP. 

About 6 months after my wedding, my mom and I finally had a breakthrough and we rekindled our relationship. It's not perfect but I feel much better having her in my life rather than not. Since I told her I was pregnant, she has been so supportive and excited. She even took the initiative to block her PTO for the week of my due date and wants to fly out to California for he birth. (She has never been out here once since I moved here 6 years ago). 

I'm happy she wants to be a part of the birth and I know I will need my mom at this point in my life, but unfortunately this means that either my parents will be in town at the same time, or my dad can't come for the first week. 

Truthfully, I would prefer if he just waited one week and then came out after my mom left. I know it's going to be extremely stressful for me on top of bringing home a brand new baby. I want my dad there, but my mom will be much more helpful with the baby, cooking and helping me with any breastfeeding questions or other "new mom" questions. My dad just doesn't have that knowledge. He wants to be there but I was hoping he would understand that I need my mom and would respect my wish to wait a week. Instead, he flipped out, telling me that I'm selfish, and I'm not being level-headed. He brings up that my mom and I have had a rocky relationship and that it's not fair that she gets to be there for the birth and he doesn't. 

I just don't now what to do. I don't want to hurt him but I feel very strongly about not having them in the same place. Especially in my tiny 1,000 sq foot home with a new baby during its first week of life.

Has anyone had to deal with welcoming a new baby with grandparents who had a volatile divorce?