Sorry to say that I don't have any info. re: her identity. What I do have is what seems to be the source of this alleged marriage, the name of the submitter, the submitter's website, and the citation, which all traces back to a big pay genealogy website that I can't afford to join.
Interestingly, she is listed only as "Hamilton" with no first name in the index of individuals on the submitter's site but also appears as "Margaret Hamilton" in the tree view (possibly a tree downloaded from elsewhere).
Then there's the surname itself...Check out all the variations on this Ayrshire site: