I made a druid, and i have a pretty high handle animal skill by this point
my question is, can i give commands to other peoples animals?
i figure at most i would need to push them but, if someone was riding their horse by me could i push it to stop, or to perform with the rider on its back?
If i encountered a guard dog, could i give it the "down" command and simply walk past?
and also, could i like secretly teach tricks to the horses in the stables at night when no one is looking while staying at a keep?
You would probably have to do a wild empathy (read diplomacy) check to get the animal to a friendly attitude before it would listen to you. If the animal was under the control of another person it would probably be considered 'hostile' if not worse/immune as well.
A well trained attack dog isn't going to just sit down next to you when its master just told it to attack. It is going to go for the jugular until it can't any more no matter what you do.
This is one of those situations that falls under the 'trying to influence another characters items/stuff' and typically requires you to deal with that characters defenses/abilities. I'd really expect the GM to work it on a case by case basis.
RAI, the animal has to be friendly to you.