[Galadriel55]

The way I understand your post, Puddleglum, is that there are actually 3 different loyalties - to Eru, to a master/authority, and to one's heart. I'd say that very often two of these are against one.
Gaima has an interesting case. He says something like "when in doubt, wisdom tells us to follow our hearts" when Gandalf refuses to give his staff to him. The 2 loyalties in conflict are to master and to heart; you don't see much of Eru here, though. You could say that since Gaima followed his heart and that caused good things to happen (ie Gandalf "woke" Theoden) and ultimately do what Eru wants, the Eru loyalty was the same as the heart one. You could prove otherwise too, though.
Huan, on the other hand, has a clear case. His heart loyalty and Eru loyalty tell him to betray Celegorm, but his master loyalty says the opposite. It's 2 to one.
Maglor had a 2 to 1 choice too, though, and he chose the one, when he listened to Maedhros and stole one of the Silmarils, killing other people in the process (a bit of the Silmarillion, like Ibrin said).
Interesting thing, loyalty...can cause so much trouble...