what skill would i use to handle a fully domestic loth-cat, as one of my players asked to have a familiar that they raised from birth, so i don't feel survival is appropriate, maybe Leadership or Discipline?

It depends on how the relationship between the player and the Loth-cat. If the Loth-cat is a true pet and the player is the "alpha" then Leadership or Intimidate vs the cat's Discipline. If it is more of an equal-level relationship, then Negotiation. I'll have to re-read the Hermit and specializations that have an animal companion and how it handles checks but I would first answer my earlier questions and work with the player to agree on a path forward.

I have one player who has a droid companion that tends to want to do its own thing. He regularly has to make Leadership rolls to convince the droid to do as requested.

Maybe Knowledge: Education? I mean if it's fully domesticated, then the "handling" rules might be fully known by the population. Just like how we can look up tons of data on how to train/handle your dog/cat. So that might be a fitting route, depending on the character.

Other than that, I'd just say pick whichever you and the player think is most appropriate, based on the relationship, and move on.

Could be a custom skill.

Ranchers from Far Horizons still use Survival for their livestock and riders use Survival for their mounts. I know the OP doesn't feel Survival is the appropriate skill, but the skills are very broad in this game and Survival is where they stuck all animal handling tasks.

4 minutes ago, HappyDaze said:

Ranchers from Far Horizons still use Survival for their livestock and riders use Survival for their mounts. I know the OP doesn't feel Survival is the appropriate skill, but the skills are very broad in this game and Survival is where they stuck all animal handling tasks.

yes but do you used your "survival" skill to handle a house cat or dog

5 minutes ago, Stormbourne said:

yes but do you used your "survival" skill to handle a house cat or dog

It's a nonsapient animal, right? The answer to this question is the same as the answer to your question.

10 minutes ago, Stormbourne said:

yes but do you used your "survival" skill to handle a house cat or dog

According to this system? Yes. I also use survival, which is based on how cunning a person I am, to ride an animal rather than any physical attribute. Which makes about as much sense.

"Survival governs a character’s ability to handle
domesticated animals, so that they may be used
as beasts of burden or as transport."

This is straight out of the rules. A cat or a dog might not be cattle, but they are still domesticated animals. While hiking I have seen people walk with their dogs where the dogs have vests on them with pouches for carrying stuff, so I guess they can fall under beasts of burden in that regard. Or transport since there are sled hounds as well.

Although I do think that Cats have Adversary 6 when it comes to being handled. Dog have an automatic downgrade of the challenge die plus a couple Boost Dice

6 minutes ago, Varlie said:

Dog have an automatic downgrade of the challenge die plus a couple Boost Dice

Not all dogs...

what would animal bond and mental bond do to the check?

20 minutes ago, Stormbourne said:

what would animal bond and mental bond do to the check?

Well in the case of animal bond there wouldn't really be a check. You have near total control of the animal and it will do what you say, or even think.

Also a bit of insight, there are specific creatures that were meant for being animal companions. The rules still consider any animal handling Survival, but you get an extra boost dice when doing so.

As well as there being talents specific for animal handling, giving benefits for survival checks. This is where I see a downside to changing the skill, it could take away some extras the player could have if they decide to pick up the specs meant for animal handling.

However, I'm all for changing up the rules for what you feel is best for your table. Out of the options you provided, I'd say discipline is what I would go for. Providing your player picks up animal handling talents and you want to keep it consistent, there is nothing stopping you from changing the wording of the talent to work for that player. Although, seems like a lot more work than needed.

Edit: Knowledge Xenology could be a good alternative as well. In the core rule book on the custom skills table it specifically mentions Animal Handling.