Okay I found some new info through Ancestry.com. I found 22 Family trees with info on them about Margaret Hamilton only 2 of which seem to be correct. So many people just add anything to their tree without even thinking! 20 of those trees had Margaret Hamilton (1565-1595) with her mother listed as Janet Beaton (1486-1522). She died 33 years before MH was born! UGH! lol
Anyway, here is what I've found out...
Margaret Hamilton's (1565-1595) parents were James Hamilton, 3rd Earl of Arran (b. 1537 in Firth Clyde, Bute, Scotland, d. 1609 in Bo'ness, West Lothian, Scotland) and Janet Beaton (b. 1545 in Scotland).
James' Father was James Hamilton, 2nd Earl of Arran (b. 1 Jan 1515 in Firth Clyde, Scotland, d. 22 Jan 1575 in Lanarkshire, Scotland) and Lady Margaret Douglas (b. 1511 in Morton, Dumsfrieshire, Scotland, d. 24 May 1579 in Scotland).
Then there's James Hamilton, 1st Earl of Arran (1475-1529) who married Janet Bethune Beaton (1486-1522).
James Hamilton, 1st Lord of Hamilton (1423-1479) married Mary Stewart, Princess of Scotland (1452-1488).
James Hamilton (1384-May 1441) married Janet Livingston (1400-1439).
John Hamilton (1361-14 Sep 1402) married Jacoba J Douglas (1367-1392).
That's the end of the line that I was able to find...