I consider myself pretty introverted. With my first, I really thought that I'd want to be alone with my dh (at the birth, and for a time afterwards). My mom and dad (not together) both ended up coming for labor/birth. I had a c-section, so they weren't in the room, but they were there in recovery.
It was great. They went home after the birth, and they didn't come back to the hospital (I delivered 1 hour from my home; 2 hours from their homes). I was so lonely!! Crazy lonely. All my friends nad family were leaving me alone, just like I'd asked, and it made me nuts.
So, the second time, I chose to deliver in my hometown (still an hour from home, but where my family and many friends live). I had a waiting room full for the birth, which was awesome. We were there 36 hours, and there was someone visiting the whole time. It was fabulous!! Even dh was surprised that it made me so happy. But, it did.
It's like birth brings out this weird side of me that finally likes people.
So, I'm on the side of tell the folks to stay home, but you'll call when you're ready to see them. Then, if you want them, CALL.