I"m glad to hear someone else shares my opinion on this!
My first was born 16 year ago and I felt the same way. As I recall, my stance was "Unless you have seen THOSE parts of me as an adult, or you have a medical degree - you are not welcome
"
Now, my mom did figure out we were in labor (she worked at the hospital and saw I'd been admitted), and my sister (DH wasn't home when the contractions started so I called her to help me time them over the phone.) So they were at the hospital, but I didn't see them until a half hour after the delivery or so.
For our second, we took our son to our Daycare provider to babysit (she was awesome and like a family memer!)- no family knew until we called after the delivery.
For our last we made an exception. I knew it would be our last, and I knew from the first two that my DH isn't really good about being my advocate and getting me what I want or need during labor. So I had my sister there and it was great. I wish I had brought her in for the first two labors!
My SIL (DH's sister) still holds a grudge over not being present for any of the births, but I don't care. I did not want a waiting room full of people waiting on me to "perform" and pop out that baby. And these are people who have walked in on me in my own home in the bathtub - and proceeded to have a conversation - so I knew what I was in for if I even TRIED to set any boundries. They don't understand boundries at all.
As others have said, stick to your guns - if you cave it will only get harder later when you try to set other boundries with them.