Daughter-in-law won't let me visit after baby is born & won't invite me to the hospital for baby's birth

My son & DIL will have their first child, a girl, later this month. DIL & I don't get along at all, haven't since day one. She prefers her mother in all things-I wasn't even included in the wedding planning, wedding or baby showers. I was an invited guest & no more. Because of the hostility, I'm not invited to the hospital for the birth & I'm not invited to see the baby until a week after it arrives. Meanwhile, my DIL's mother (granted, she is a pediatrician) will stay w/my son & DIL for a whole month while I can only visit for a week & have to stay in a hotel. My son said that my DIL wants only her mother there- her mom gets to stay in the house. The house has 4 guest rooms & is big enough for both of us mothers. I resent that her mother gets special treatment, but my son doesn't want me to start drama. He says I'll have plenty of time to spend with my new granddaughter in the future & that DIL feels that since this is mom's 1st grandchild, she gets dibs. DIL is also an only child.