My mom got angry

So we have decided that when it's time to go, we don't want anyone else in the hospital with us, just my husband and I. We feel that giving birth and bonding with the baby right after is such an intimate moment that we want to be just the three of us. I casually mentioned it to my mother and she got ridiculously angry, acting like a martyr and saying things like "oh well I'm just your mother, why would I be needed there", "I bet your dad's new girlfriend will be there" etc... I explained to her that she's not the only one, that my dad or my husband's parents aren't allowed to come either and neither is no one else. Everyone can come see the baby when we get home (unless we need to stay in the hospital longer for some reason). She still seemed to take it personally and I don't know what to do. If her reaction was like that, how will the others react? My father and his new wife are so excited about us having a baby that they will definitely be offended if they can't come to the hospital... I'm almost at the point when I'm considering not even telling about the birth to anyone until we're comfortably home! What should I do? Are we wrong for wanting some privacy?