Can Aura of Dominion be used with Inspire Creatures?
Yes, you can use Aura of Dominion to repeatedly trigger Inspired.

Basically, when you activate the ability, you tap the enchanted creature (and pay 1 mana) to pay for it. Then when it resolves, the enchanted creature untaps and the Inspired ability triggers. Then the game has basically returned to the state it started in, so you can do it until you run out of mana.