I have over 20 years experience working with pregnant and postpartum families as a doula, antenatal teacher, breastfeeding counsellor - and I also run classes online for grandparents.
The daughter is not being "selfish" as some have said - she is however making very unrealistic promises to herself. The first three months of the baby's life are sometimes called the "fourth trimester of pregnancy" because the mother needs help with everything that she doesn't have time for while she gets to know her baby, learning to recognise the cues and to feel relaxed and above all confident. ALL human societies have recognised the need for new mothers to be allowed to rest quietly with their baby, being brought food and not having to worry about housework or any other chores.
Unfortunately some grandparents do interpret this need as giving them a right to interfere, to lay down rules about "how we did it in our day", to chatter constantly when the mum would prefer peace and quiet, offer unhelpful and unsolicited feeding "advice", to manhandle the baby, and to pressurise the mother and her partner to separate the baby from the mother on the pretence that "mother needs rest". Such pressure can be very unwelcome because a new mother is instinctively attuned to her baby, typically, and contrary to what people think she may not thrive by being separated from her baby - and the baby certainly doesn't.
It could be that this young mum to be has heard stories from her friends about overbearing grandmothers and wants none of it.
But she needs to be aware that these days nearly half of all births end with a caesarean and if that's her journey she really will need a lot more physical and practical help than she realises.
The message to get across to her is - if she needs help, just ask for it! The word "visitors" however suggests that the OP expects to sit on the sofa holding the grandchild and being given cups of tea...instead, it would be smarter to gently offer practical and targeted support in the home - cleaning, laundry, cooking a shepherds pie rather than insisting on the right to hold the newborn. "When can I come and help out" sounds a lot more attractive than "when can I come and visit".
If she still isn't interested, how about offering long-distance support such as getting her shopping delivered?
I think there must be more going on here especially with the MIL and not the OP. Daughter may feel she has to send out the same message to both sets of grandparents to make sure she isn't interfered with by the one she's more worried about.