congratulations on the coming baby, Amber! And what a beautiful attitude you have about the birth and so forth!
Generally speaking, I think it's mainly up to the parents, especially the mother since she's the one actually going through labor and delivery. I was wanted in the room all the time when my DGC were born, but I know some parents-to-be don't want anyone else there at all.
I've heard a lot about the 4th trimester though I've yet to know anyone IRL who followed that idea. I think it has come about cuz dads are so much more involved in childcare, these days. It's often hard for mothers and MILs to accept, but young parents often don't feel they're going to need our help, they way they might have back when few dads shared in the babycare. My own DH took off a week from work for each baby, but wasn't really very helpful. I definitely needed my mother and MIL the first few days. If he had been willing to share in the babycare the way many men do today, I wouldn't have needed them as much.
Still, I would have been eager for them to come visit my new baby though only for brief periods, just as I felt about other relatives. But that's just me. I know that not everybody feels the same way.
So I'm glad you and DH are going to abide by the parents' wishes. And I agree with those who say you need to stay out of DD's and SIL's decision. It's lovely that you're thinking of Nanna and the GF, but it's up to DD and SIL to tell them their plan and figure out how to handle GF's visit. Honestly, I feel he should be given a chance to change his plans and come after a month has passed, if he can. Sure, that means he'll miss meeting the baby when he/she is just born. But it would ensure his getting more time with baby than just one meeting. I think you need to trust the young couple and the other grands, though, to work all that out, themselves.
Chances are, the young couple will change their minds, as others have said and reach out for help/visitors a lot sooner than the one month mark. However, even then, they may stagger it (I've also heard of this). For example, they may invite you and DH after a week or so, then the paternal GPs after two weeks or so and so forth. Also, I've read about couples who say they loved having that period to themselves. So I don't think we can predict for sure. Please just go with the flow and realize that things may/may not change once baby is here.
If Nanna expresses any hurt to you, I hope you'll let her know that it has nothing to do with her, that it's increasingly common today. IMO, you don't need to do anything beyond that.
Wishing you all many joys with the new baby!