I think Inquisitions can be chosen in any case where you're allowed Domains, but I need to double check the rules.
Yup, here we go.
While a cleric or other domain-using class can select an inquisition in place of a domain (if appropriate to the character’s deity), inquisitions do not grant domain spell slots or domain spells, and therefore are much weaker choices for those classes. These other classes use the appropriate class level as their inquisitor level for the purpose of inquisition granted powers (clerics use their cleric level as their inquisitor level, and so on).
So Inquisitions and Domains are purely interchangeable. Of course, to choose Anger Inquisition you would have to worship a LG-friendly god with Strength, Battle, Weapons, Wrath, Destruction or Disaster in their portfolio. A Chaldira worshiping Temple Champion, for example, can indeed Rage.
EDIT: An even better god would be the Son of Torag, Trudd. God of Strength, Defense and Bravery.
A Temple Champion gains only the base power of her chosen domain. She wouldn't gain the 6th-level power, so she couldn't rage.
Also, Inquisitions haven't associated blessings (yet), so the paladin wouldn't gain that, either.