Suppose a mount does not know the Sneak trick. Could Ride be used to get the mount to use stealth? The specifics of the situation:
Character is a Goblin Hunter, Level 4 with a Wolf animal companion. For the Teamwork Feat, I could choose Stealth Synergy.
So, as a rider, is it possible to convince a mount to perform a trick it does not know using a ride check? Or would that require a DC 25 Handle Animal check to push the animal? Basically, my ride check is +18 and my Handle Animal check is only +12, so I am looking for a way to use Ride instead, if it exists.
Best Answer
Ride can't be used like that
I could find no item, feat, trait or anything else that does this when searching Nethys (the official SRD source) nor d20pfsrd (better for finding 3pp options) for Ride, Push, and "Ride Push".
Unless you're using Spheres of Might
The major 3pp alternate rule supplement Spheres of Might (the sister project to Spheres of Power) has the Beastmastery Sphere; when choosing this, among the other benefits, is the option to supplement Ride when Pushing a creature you're mounted on. Unlike some 3pp content, this is not typically something that can be approved one-off by the GM because it's a alternate system, not simply additional character choices.
Just teach them the Sneak Trick
Rather than searching for an obscure choice that would let you spend Move actions to get them to do things, you can just (pretty easily) make the DC 15 Handle Animal check, spending one week of downtime, to permanently give them the Trick itself. This will be one of the 6 tricks that you can teach them (their starting Int is 2) that are separate from the Animal Companion Bonus Tricks (of which you should have 2 at the moment).