I put a dog standing into a minecart, after a while the dog was sitting inside the minecart (not sure what triggers the bug). I broke the minecart and the dog started walking seated, I wasn't able to right click it to make it stand up. After quitting and entering the world again, I'm able to stand the dog up. Seems to only affect certain dogs, as the other dogs, that were also inside a minecart, weren't bugged. The minecart was put above an unpowered powered rail.

Below you can see an image of the "initial position" (coords are different).