I'm playing a hunter and taught my animal companion the Skirmisher Trick Vengeance Strike. But when I tried to use it in the game, my GM said it couldn't since the trick uses an AoO which my companion had already used that round. But that's not true, is it? Here's the text for Vengeance Strike:
Vengeance Strike (Ex): The Ranger can use this trick as an immediate action when an enemy adjacent to him hits an ally with a melee or ranged attack. The Ranger can make a single melee attack at his highest base attack bonus against the creature who attacked his ally.
You are correct in that that trick does not use an AoO. If it did, the word "opportunity" would certainly appear somewhere.
OTOH, the skirmisher "hunter's tricks" are not animal tricks and cannot be taught to an animal companion. That's why they all say "the ranger does this, the ranger does that" specifically. Really they should have called them "talents."
They can be taught to an animal companion if the PC is a hunter.
At 1st level, a hunter forms a bond with an animal companion. A hunter may begin play with any of the animals available to a druid. This animal is a loyal companion that accompanies the hunter on her adventures. This ability functions like the druid animal companion ability (which is part of the nature bond class feature). The hunter’s effective druid level is equal to her hunter level. If a character receives an animal companion from more than one source, her effective druid levels stack for the purposes of determining the companion’s statistics and abilities. A hunter may teach her companion hunter’s tricks from the skirmisher ranger archetype instead of standard tricks. The animal companion can use skirmisher tricks when commanded, a number of times per day equal to half its Hit Dice plus its Wisdom modifier.
Whoops, you are correct again. My bad.