We didn't have rules as such, but I had asked family during the pregnancy to not visit at hospital, we were happy to have visitors at home but I just wanted DH and DD1 when DD2 was born.
In the end DD2 was early so I did need my mum a bit because she was buying things that we didn't have, like prem clothes. So that was fine! She also picked up when I needed to be left alone and would just up and leave. But one of my SILs was so out of line. She barged in unannounced with her two kids who screamed and carried on the whole time, jumped all over me (I'd just had an emergency CS) and then she had the balls to get angry when she couldn't see DD... Who was in NICU.
If we ever have another I will be like a PP and just not tell anyone when it's happening.