I have 2 pets. They live in the same household. Mine keep playing together I don't know if it's just a coincidence like they start playing in front of each other or not!
Are they supposed to interact with each other?
Pets will help dig up useful rewards, but other than that they can't interact with each other. They can roam around your yard as freely as possible, digging gold, but they won't meet up with each other and do some "animal talk". I think it's just a coincidence that they are playing individually at the same time.