Relatives after birth

Hi guys, I'm a FTM... me and my husband were talking yesterday about when other relatives come in to visit after birth?

I was thinking of having my husband and my mum with me as birthing partners and he said "ok well my mum (my MIL) can wait outside and come in and swap with your mum as soon as the baby is born" .

I've told him that it's not an immediate thing, the placenta needs to be delivered and I would wanna have a shower or something first (as I've been warned how messy it gets!) .

I said to him I don't see the point of his mum waiting in the waiting area (if there even is one.... is there normally waiting rooms in delivery wards??). I said she could be there for hours or days and he said she wouldn't care and would want to be there. I said it would only take her 15 minutes to get to the hospital why don't we wait til everything's done and then we can call her (and my dad too!) to come then. He said because he doesn't want to tell her over the phone.... I feel a bit like I'm being selfish like I don't want to have to rush because she is desperate to come in? And what if I need my mum in there for longer? And I want him to be with me all of the time not going out and giving her updates...

What will realistically happen? Do midwives have a say? Is there anywhere to wait anyway? What should I do?