It has to do with terrain and other obstacles. If there is something blocking the back area of the animal youll get the quick skin animation. You can force this to happen by parking your horse right by it. This was a 'hack' from the first game, too.
After you reach a certain length the game tells you that it wont grow any more unless you drink hair tonics. The best way to do that is drink a tonic then take a coach somewhere far away.
The trapper has them. You don't need to buy them from him or anything, he just already has them ready to craft with (all you lost out on was the money you'd get from selling them to him)