Limiting visiting time?

Aubrey • 26, married 06/2013, 1st babe born 9/17/2017 💜, 2nd babe born 4/20/2020 💜

So we're quickly approaching baby's arrival and I just want to have time after she gets here to rest and figure her out. Would it be wrong of us to limit visit times that first day to 30-45 minutes? We have soooo much family and just our parents will take up like 2+ hours. We are having her at a birth center and will likely go home hours after I give birth so I don't want a million people in our house pawing at our baby before we've even had a chance to be with her. I'm not sure how to politely tell people that?