They are not mutually exclusive. Just take the quest to help one of the sides and kill the frog, then take the quest to help the other side for the stone. This is one of the places where amelie becomes a double agent
Mutually exclusive quest seems to be the one for Griida and Coruscan. You either have to kill him, or you need to beat up an enemy stack to help the poor goblin show that he's a good husband.