I finally got the second ending! For anyone struggling: You need to pay careful attention to Udyr's sprite (and sounds). Give him pets when his ears are down and his lil mouth closed and he's calm. Get his attention when he's looking riled up. Give him pets when he calms again. I know, buddy, I know the other animals at the park are distracting, but we'll get through it together.
There's a lot of love in this game and that comes through wonderfully. The sound effects were great and the art is so, so expressive—even, somehow, the screen transition, which is so beautiful that I actually linked the game to a couple friends, "Look how lovely the transition is!"
All in all, a great little game.