What you could do is run with their inability to combat the wasps, and turn it into plot. The first time they encounter the wasps, they get severely injured and are forced to flee. You then have a followup of them looking for a way of combating them: be it fire weapons, magic bug spray, or whatever.
Just try to make it clear to the players that they're meant to be insurmountable in the first fight.
It Should Be A DC 10 Handle Animal
Here's the rules from Handle Animal:
This task involves commanding an animal to perform a task or trick
that it knows. If the animal is wounded or has taken any nonlethal
damage or ability score damage, the DC increases by 2. If your check
succeeds, the animal performs the task or trick on its next action.
So, does "squeeze into a cave" count as its own trick, or can you use an existing trick to do that? Ultimately that's the DMs call, but my interpretation is that it should be a DC 10 Handle, using the Heel trick:
The animal follows you closely, even to places where it normally
wouldn’t go.
Squeezing into a cave certainly is a place that a Horse normally wouldn't go, but:
- The Horse isn't being threatened by anything in the cave, as it's you doing the handling and it knows you.
- It's capable of moving to the location you want it to without taking damage. It sounds like it may not even need to make a check to squeeze, based on your description. (Checks aren't required if it has half the necessary space, so a one square wide tunnel in this case.)
- It also has taken no damage that you've mentioned
Based on those things, no special conditions apply here. Given that, I would rule this as a DC 10 using the Heel trick. (The Come trick has similar wording and would also work if you don't know Heel.)
If you don't have either of those tricks, then it gets a bit trickier. There's no rule on simply leading an animal where it doesn't want to go specifically, and in the absence of training there is a stronger case to require the DC 25 Push check.
Best Answer
An "animal companion" is a special ability that mostly druids and rangers have. It is irrelevant to this discussion as your rogue does not have it. See What feats can I use to get a companion of any sort? for a list of abilities that actually grant companions in the technical sense; these guys stick with you and help you because they're your nature buddy. The rogue, however, is basically in the same boat as someone who wanders down to the local zoo and convinces them to sell him a tiger. He has no specific control over it and it has no specific reason to care about him.
A PC can purchase and try to keep around any other kind of creature that's available for sale and they can afford, from animals to human slaves. Note that things are not available because "they are in a book the player has" - you're the GM, put on the big boy pants, you control the game world and what is available and how in the markets of your game world. If such a creature is available by sale or by capture, whether you can use them effectively and whether they kill you in your sleep or not has a lot to do with other rules systems and roleplaying.
If you have an animal (a monster of type "Animal" - not magical beasts, not anything else) you can use the Handle Animal skill to teach them specific tricks over a long period of time and to try to command them in combat. There are a couple magical beasts that have an exception stated to this (hippogriffs, familiars) that can have Handle Animal used on them in specific circumstances.
If you have anything else, then it's pretty much you convincing them through other means to help you out. This is one part GM fiat, one part bluff/intimidate/etc (for intelligent creatures). Charm or dominate, or the Leadership feat, or other specific rules in the game that allow for influencing other creatures apply as normal.