OP, you say that you have a 3yr old - so you've fairly recently been through what your dd is about to go through.
When you had your 3yr old, when did your dd want to come to visit you? and when did you want her to come and visit you? Did you have different expectations then? Or if your mum is still around, when did she visit you and when did you have visitors in hospital?
And did she see you early on, maybe in pain or struggling against tiredness or having a succession of visitors and not being able to get started properly on breast feeding or getting out and going to the loo without blood leaking out all over the place or who knows?
But she might have been there and thought - if it ever happens to me, I'd like it to happen differently.
People are expecting to stay less and less time in hospital these days - ds1 is 5, ds2 is 2 and even between those two, first time around people were talking about staying in hospital for a day and then an overnight and going out. Second time, the overnight had shifted to being the night the baby was borning and going out the next day - as it was I stuck around for 4 hours before going home. She might be hoping that the same will be happening for her - just enough time in hospital for getting tidied up and sorted out and then home. There must have been a point when you were having your 3 yr old between the baby being born and getting washed afterwards, getting checks done, having a snack, that you were just getting over giving birth and then you were relaxed and ready to see people (other than partner and medical staff!) - and that if people had come in earlier you would have felt uncomfortable. Your dd doesn't know when that is going to be for her so she is trying to make sure that she isn't caught out by anyone turning up when she isn't ready to see them.
Could you maybe say to her that, if she ends up in hospital for more than a day, then could you pop in during visitor hours just for 10 mins, bring her anything she wants and see both dd and baby.
Do you think she is worried that you are going to try to turn up as soon as the baby is out, before she has had a chance to have a shower or get cleaned up or talk through personal stuff with the doctors and midwives or even have a cuddle with the baby herself?
There are lots of posts on here where new mums have had horrible experiences where their mum or MIL has barged in and taken over the baby while the poor new mum who has just had the baby can't get their baby back or is trying to breast feed for the first time with an unwanted audience or just wants to go to sleep while the baby has a sleep and can't because there are people there.
It's worth reading some of them to get their point of view. If you do ask your daughter again, you need to be sure that you will reassure her that you won't visit until she is ready to receive visitors, whenever that may be for all the different reasons, and let her know that she can change her mind at any time, you still love her and will be there for her.
Yes, she's your dd. But she's also got a great extra load of horrible hormones whizzing around inside her, if it's her first child she has probably read or heard about all sorts of scare stories, is worried about how labour will affect her and how she will cope afterwards.
and remember too that it is very easy to tell people before the birth that you don't want visitors and then, if things go well, you feel OK, you can change your mind and people will be pleased. But, if you tell people that you will have visitors, but things don't go as well as you hope, or you are feeling rotten, whatever, it is much more difficult to tell people not to come once you have already told them that they can IYSWIM. So hopefully she is just giving herself the space in case she needs it but knows that you would love to come if not!