Quoting
jk
ok, obviously ownership of the dog is important. If there is no true single owner and it is simply a household dog, the owner/tenant will likely be seen as the owner of the dog. Beyond that, unless the OP has a controlling interest in the home, the person with such interest can impose a no dog rule. While simply taking the dog to the pound may be an issue, ultimately they do have the right to force the dog's removal, one way or another.
and by the OP's referral to a kennel, I am picturing a cage or some similar containment at the residence and not an kennel such as one would board a dog at.