I would have no problems with it, but (and this is a big "but") you need to booster-train her in your car first. Once you are certain that she can sit correctly 100% of the time for the longest trip that gma could possibly take her on, then you can take the booster to gma's house.
Caveat: Be prepared for the possibility that you'll need to buy a harnessed seat after all. Some kids are ready at 4, but not all of them.
Illustration: My DD went into a booster at 4y7m b/c she broke her arm. She sat perfectly, even sleeping, in her Vivo on trips up to 2.5hrs (the longest trip we took while her arm was broken). However, I also have a niece that at 6y6m, still would not sit correctly. My sis had to keep her harnessed until 6y11m, when she outgrew the Maestro (a FR85 was out of the question financially). My sis still has to constantly remind her to stay put and leave her belts alone. Her sisters (all 3 are neurotypical) reached booster maturity at 5yo and at nearly 6yo.
Kids reach this maturity at vastly different ages. You might be lucky and have a kid who is ready at nearly 5yo. Just be prepared that she might not be ready yet. Both are developmentally normal.