Interestingly, I am in the same business, except that we are principals (we rent out our own apartments) and not a listing agency like HomeAway. I can tell you that we would NEVER engage in the type of behavior that you are describing. I just lost a very high-value rental because the prospect would not book without seeing the apartment, and our policy is that we do not show apartments when a guest is in residence.

Even for maintenance issues, we always ask in advance for "permission to enter."

A big to your landlord. Unfortunately, unless you have read all the fine print, it is quite likely that the contract allows them to do this.