I sensed that these relatives might have emigrated as you know so little of the irish locations other than Co Antrim.
1796 source for Flax growers in Ireland gives
No McMillan or McMillen
Young James Ballyrashane Antrim
Young John Dunaghy Antrim
Young William Derrykeighan Antrim
1823-1840 the tithes applotment Books are on line by civil parish. I decided to search just those parishes in Griffiths valuation where both McMillan and Young were both in the same parish. There are 6 such parishes and that seemed the best gamble to quickly find the links.
Ballymoney
no McMillan
Young, Charles Townland: Carnanreagh Year: 1825
Young, Robert Townland: Ballynamoney Year: 1825
Young, Robert Townland: Lislagaw Year: 1825
Young, Robert Townland: Millquarter Year: 1825
Young, Robert Townland: Newhill Year: 1825
Young, Samuel Townland: Ballynamoney Year: 1825
Young, Widow Townland: Ballynamoney Year: 1825
Young, Wm. Townland: Stranocum Year: 1825
Carnmoney no McMillan yes McMullan, no Young
Carrickfergus no McMillan, no Young
Killead no McMillan yes McMullan Young, Samuel Townland: Ballymather Year: 1827
Shankill ie Belfast Co Antrim None
Templepatrick the same townland Craigarogan none
Tickmacrevan Lower Glenarm Antrim as suggested by Ballydw
no McMillan , no McMullan no Young
So that was all disappointing, so I tried the flax growers list of parishes
http://www.irishgenealogyhub.com/antrim/tithe-applotments/derrykeighan-parish.php#.VZa2fkuDoYU No to McMillan yes toMcMullon and Young
http://www.irishgenealogyhub.com/antrim/tithe-applotments/dunaghy-parish.php#.VZa3eEuDoYU no McMillan yes McMullan, and no Young
http://www.irishgenealogyhub.com/antrim/tithe-applotments/ballyrashane-parish.php#.VZa4hkuDoYU no McMillan yes McMullan, and Young
So more disappointment for a quick solution.
I haven’t the time to go through the tithes for Tyrone civil parish, but it remains a possible source for you.
So make what you can of it . it looks like you may do the Young tree easier than McMillan
Has anyone else done the family history
Good luck jimG