I have the same James Maxwell. I'm decended from his son William born 1-26-1813 in Ohio. I have been researching several stories about the family including James as a Royal Marine from 1791-1802, James the Englishman, the family in Germantown NY from 1805 until 1810, and The ship Lydia. I have run into many dead ends and brick walls, but also discovered some gems along the way. I would love to share info with you. I do not have any more information on their time in Ireland, but have tracked the family through the USA over the generations. Let me know how I can help.
I found an interesting note on the Ship Lydia. Google Ship Lydia and Henry Treadwell (the owner) Alexander Hamilton argued a case involving the ship.
Take care. ~ Mike Maxwell