In my opinion, there is nothing wrong with multiple girls/boys in a family with similar names. In my family we have a ton of Marys, Maries and Kathleens (my middle name is Marie), and Grace is common in my DH's family--pretty much all of the granddaughters have Grace in their name somwhere in honor of his late grandmother, whom everyone adored.
We named our daughter Mary Grace (for my mother and DH's grandmother), and DH's brother has a daughter Mary Elizabeth (who is 16 years old, but still, they are first cousins). We do call our daughter Grace though.
I think there is nothing wrong at all with you sticking to the name you have chosen for your little girl. DH and I had decided years ago (we have been married 17 years!) that if we had a daughter she would be called Mary Grace, and we didn't let anyone else's choices through the years, all the Marys and Graces that have come, change that! Nor have we ever had any bad feelings towards any of our cousins or siblings choosing those names.
If I were you, I would not change your DDs name for the world. She is your precious little Grace, and you have every right to keeping her name. If your aunt and uncle also want to use the name for their DD, that is up to them, and they have no reason to be upset with you imo. (I also think that the world could never have enough beautiful little Graces in it!--but I am biased!
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