P.G.
Maybe I'm the weird one, but why is it a problem for her to spend time with the grandparents if the grandparents are already awake? Unless they aren't "kid people", most grandparents ENJOY the time they spend with the little one. It doesn't matter if it's not their "responsibility" to spend time with her in the morning; if they love her, it's just a normal relationship. Ask them what they'd like.
Let her know the rule - if grandparents aren't awake, she can get mommy. Or you can set an alarm.
It's another story if there is a reason that you don't want them spending morning time with her. But then why would they be spending time with you if you didn't want them around her.