When DP's DGD was born, her mum had a really tough time and what was going to be a tranquil water birth at home ended up being an emergency CS.
Poor mum had laboured for over 24 hours and was utterly exhausted and very, very upset. She didn't want any visitors other than her own parents and sisters for 48 hours, because she was in such a bad way.
Despite that, DP's ex basically camped out at the hospital and went as far as to move chairs so she could sit right outside Mum's hospital room (they'd given her a single room) and DP's son brought the baby out she could meet her.
This wasn't good enough: the ex stayed at the hospital, apart from going home to sleep, for nearly 36 hours. In the end, mum gave in and let her in to see her, and she stayed so long, taking shedloads of photos, and generally being very intrusive, until the new parents insisted she leave.
She was just the same when they got home, constantly turning up unannounced and overstaying her welcome, until they were forced to give her the stern word and insist that she didn't come round unless they'd agreed to it first.
It irreparably damaged her relationship with the baby's mum. The couple have now split up, and she only has contact with her DGD when dad has her. She is very pissed off that we go and visit them in their new home and have a "normal" relationship with them both.
I think if a new mother doesn't want visitors, or only wants her own family to visit, that should be respected. She's the one who's done all the hard work, and suffered the pain and indignity, after all.