From a US Presidents Project standpoint, I doubt we will easily find the connection through the Grant family. The President's immigrating ancestor was Matthew Grant, who came to the colonies about 1630 as part of the Puritan Great Migration. https://www.wikitree.com/wiki/Grant-201
Working through what appears to be your Grant heritage, your immigrating ancestor was John Grant. There is a book written by Ruth Winona Grant, "The Loyalist Widow, Elizabeth Grant; Her Family, and The Area in Which They Settled"
John Grant, had been loyal to England and the King during the Revolutionary War and he had fought for the King's army. He was apparently wounded and died near the end of the war in 1783. Since they had been Loyalists, the family was no longer welcome in the new United States and the King's American Regiment helped relocate them into Canada. The book is about Elizabeth, her remarriage and her Grant children.