When I lived in apartment will parents as young we brought Jane and sneak her in. The Management never. Plus we weren't the only ones. Almost everyone in the apartments had pets.Cats, dogs, you name it. Everyone used to go the playground and let they dogs play. Now we just moved in our first house in years. And now Jane is still run runs around like a maniac.

Because her first and very own backyard. But have to share with the new puppy.
Maybe you could ask your realtor if you could pay a extra fee for your pets?
Just suggestion!