It shouldn't be possible to interact with your dog apart from the commands while in a hunting stand.
Yesterday I tried to play with the dog while I was in a hunting stand on Hirschfelden. The animation started and I got teleported to the ground underneath the hunting stand between the four poles. And I couldn't get out of the structure.
Obviously, this is avoidable but just not interacting with the dog, and if you do you can fast travel out of it.