I don't understand the PPs saying I wouldn't be able to wait. You bloody well have to wait. That's completely selfish and not thinking of anyone but yourself.
Slightly different situation here, as we live in a different country to both sets of GPs so both would have to come and stay/stay in a hotel, which I just couldn't imagine making them do. ILs are on another continent and MIL once hinted she'd like to be here for the birth, which, given the distance involved, would mean a long stay, of at least a month. I was adamant that I didn't want either sets of GPs there, partly due to different cultures and ways of doing things. I wanted a short amount of time for me and DH to get to know our baby and figure out our way of doing things. I also wanted my DM to be the first to come and stay - not because I dislike my ILs, or even because of the distance - but because I knew she would be the most helpful to me.
As it happened, DS arrived late, and DM arrived only 1 day after he did, while we were still in the hospital. It was THE BEST THING ever. We got home, DH and I curled up on the sofa, DM cooked, cleaned, made me go to sleep, brought us both tea, plates of cut up fruit, whatever we wanted. Yes, she had her time with DS too, but she was an absolute godsend to us both. She stayed out of our way too, she wasn't always 'there'. She completely understood what we needed. If DMiL had been there, she may (probably would) have been just as helpful and understanding, but I would still have felt that she was a guest in my home, in a way that my DM isn't and that I had to look after her.
My DF (separated from my DM) also wanted to come asap but he decided to give us a week after my DM left so that we had our own time. When he came, it was just as lovely, but much harder work. I felt like I was looking after him more, although he was very helpful in his own way whilst making more work by being helpful in said own way
My point is, that yes, everyone wants to see the baby, but this time isn't about the baby so much, it's about the Mum, and what she needs. It may seem unfair, but unfortunately, a new Mum is probably going to want her own mum there over anyone else. And if it's her best friend she wants around, than that's what should happen too. Everyone else should understand, including DH and the ILs. I know I would, if it were my DiL, even though I would want to be there straight away.
That said, you might feel absolutely fine after the birth, have a pretty easy baby from the start and feel ready for visitors earlier. In that case, you phone them up and say, come on over.