As others have said you'll have a great time but you're spreading yourselves pretty thin.
If you're never making it back to Scotland, then Dornoch by all means.
But I think a much better option would be to leave out the Highlands, and add the likes of Prestwick, Western Gailes, Crail and Elie.
Personally I think in any event a day of Prestwick and Western Gailes would be more interesting from an architectural perspective than the two Troons.
Then if you can, try to get back to Scotland and do a trip through the north-east and the Highlands, including Royal Aberdeen, Cruden Bay, Lossiemouth, Fraserburgh, Dornoch, Brora, Nairn etc.
Have fun.
Andrew