This is really a tough issue and we have found a few ways of dealing with it over the years. For what it's worth, here are some of those experiences:
(1) Having a good housekeeper is critical, because they are often the only people who actually see your house. And I touch bases with ours fairly regularly to see how people are treating the house. Also a good idea to ask them about things that won't be treated well. Believe me, they have seen it all. If the housekeepers don't report damage, nothing hapens in terms of compensation.
(2) We all hate screening renters, but we have started doing it and no one seems unhappy. I have our company send a one-page questionaire to all renters and they respond with how many adults and how many children will occupy the house. Then I usually call the house on a Friday or Saturday night to inquire as to whether they found everything they needed, whether the house was cleaned properly, and how they were treated at check-in.
I once called the house on a Friday night and asked for the adult in charge. Loud music and shouting in the background, long delay for anyone to come to the phone. Finally, an obviously very young woman got on the phone and said, "Thank yuuuuu soooo much for taking a chance on these girls." Flags up everywhere, so I called the management company to check it out. Sure enough, there was no chaperone and the housekeeper stopped counting at 20 cases of beer bottles. I put this renter on the black-ball list for the future. We now have three people on that list.
There are several things to beware of: (1) Last minute rentals, especially in the spring and the first week in June. These are often college students (who don't plan) or senior graduation trips. I'm sure there are some good ones, but we haven't had a good group like this to date. They are typically inadequately chaperoned, drink excessively, and have no regard for themselves or your property. (2) The other thing to avoid is a two-night rental on a weekend such as New Year's Eve, Halloween, a big football weekend, etc. (3) People who start asking for a discounted rental from the outset, because they will be looking for some reason to justify one later. Fortunately, this doesn't happen too often.
(3) All management companies have strengths and weaknesses, but there is something to be said with hiring a good one close to your house, then trying to work out problems rather than jumping ship. These companies value long-term relationships and desirable properties. They are usually doing the best they can with a very limited labor base and high stress situations during the summer and holiday seasons. The property turnover alone is a stress test. I have pinpointed specific individuals that I know are trustworth and responsive and then cultivated strong relationships with those individuals. Consequently, they will move heaven and earth to take care of us. For example, the housekeeper gets a free week; my key contacts get little gifts for new baby or a special birthday; the office gets the biggest box of See's Candy I can order during the holidays. These are inexpensive gestures in the long run, but it lets people know you think of them as something other than a jobber.
(4) Ask your management company for a list of your renters from the previous year and send holiday cards to them. I like to get those folders and include a favorite photograph of Grayton Beach or of Conch Out. We now receive lovely holiday cards, often with a family picture from their time at Conch Out, and we also have a growing list of those who are repeat renters. They are our gold! And makes it very easy for you to check and confirm who is a repeat renter and who is not.
Hope this helps. Beachrunner, I would tend to agree that you need a new company. Perhaps the one you now have is somewhat limited in terms of clientele and so more concerned with keeping renters than managing your lovely home as it should be. Good luck!