Hope for Undomiel.

[The Saucepan Man]

I mean, if Gimli was able to enter (presumably by Galadriel's support) couldn't Galadriel do the same for her grand-daughter?

Well, it's possible I suppose. But had she been allowed to go to the Undying Lands after Aragorn's death, she too would have died in time just like Gimli (assuming he made it there) and the other mortals who sailed West (Bilbo, Frodo and Sam). She had chosen mortality and, as I understand it, that choice was irrevocable.