Right after your baby was born, how much time did visitors spend in your home?

I’m only 12 weeks right now, but based on things our parents are saying I’m already concerned about this. My parents are extremely pushy / self-centered / controlling, and they’re adamant that as grandparents, they have the uncontestable right to be around the baby whenever they want, do whatever they want with / to the baby, and insist on how we should raise our child. They work less than 2 miles from our house, so I’m worried that they’re going to expect to be here all the time. I tried to subtly tell my mother that the new baby is just going to sleep most of the time, and she said “But it’s always ok to wake up a sleeping baby to play with Grandma!”

My husband’s parents are not at all pushy, but they live far away and will be visiting for three weeks shortly after the baby is born. They won’t have work or any other time commitments, and obviously the reason for their visit is to see the new baby (who they won’t see again for several months after), so I’m concerned that they’re going to expect to spend almost all their time here as well.

I want the grandparents to be able to see and spend some time with the baby, but I also want us to have time to bond with the baby by ourselves, and I want plenty of rest and quiet without feeling like I have to entertain visitors.

Right after your baby was born and everyone wanted to see / hold / play with him/her, did you limit visitor time? Did you limit visitors by number? How did you politely tell people they were hogging your baby? How did you subtly kick people out when they’d been there too long?