Can our landlords dictate where we keep our dog when we are not home, provided that we are doing our due diligence to protect their property?

That depends. The landlord can't make you crate your dog, or lock your dog in a room, if that's what is being demanded. However, the landlord can insist that you NOT keep your dog tied up outside, if that's what you're doing because, for one thing, it's illegal.  The landlord can also insist that you change where you keep your dog if the dog constantly barks while you're gone. What exactly is your landlord demanding, and why?