Ghorgath:
Okay another way of doing this is which skill is closer, animal handling or.....
The kind of training you're talking about doesn't require a skill test or single skill proficiency. In terms of time-scale, it's so far beyond even an extended or long test that making a check is just not a factor. In terms of actual skill proficiencies, it would likely involve a great many skill tests of different types; Intimidation for discipline, Athletics for PT, Insight and Perception would also likely be involved and then there's the subject material you're trying to teach; History? Medicine? Survival? Combat skills are obviously covered by Class and Level. As a GM, I'd call it as a down-time activity like crafting an item.
As for the utility of Animal Handling; it's every social skill rolled into one...except only for animals. Want to determine what horse might do next? Don't roll Insight, roll Animal Handling. Want to calm an angry wolf? Don't roll Persuasion, roll Animal Handling. Want to front up to a grizzly bear and get it to back down? Don't roll Intimidate, roll Animal Handling. Yes, there's an element of training animals in the skill, but that's not what the skill will actually be used for; training an animal would again be a down-time activity that doesn't require a skill check (though as GM I might require proficiency in Animal Handling to train animals).