So the rules for the usage of Handle Animal on animal companions with a 2 Intelligence are pretty straightforward, and many people bump up their companions Intelligence to 3, but what about exceptionally intelligent companions?
For example, a 9th level Human Paladin with a bonded mount and the Eye for Talent alternate racial trait. If he applied the racial trait to the companion's Intelligence (which is base 6 for paladin mounts), then applied both ability score increases to Intelligence, you'd have a mount with an Intelligence of 10, more intelligent than a good number of fighters out there. You could add a headband and get even higher.
By that point, the creature has pretty much unarguably reached the level of sentience. Would you still need to use Handle Animal to 'push' your companion into something he didn't want to do, or would Diplomacy become the way to deal with social interactions with your companion?
"Creatures of animal-level instinct have Intelligence scores of 1 or 2. Any creature capable of understanding speech has a score of at least 3." - pg 16 PCR
Any animal companion that has a 3 or higher Int arguably could be convinced to do something via Diplomacy or Intimidate and might even resent being pushed via Handle Animal. That sounds like a DM call though.
Blog post on this topic.