Sorry kryalkastle, I didnt mean to upset you in any way and I now have a better understanding of the position you are in and feel for you. It's a crappy situation when you are the frontline for others and therefore cop abuse that should clearly not be directed at you.
If you are having problems like this frequently then perhaps you should suggest to your boss (or bosses) that they need to follow up the reason why you are getting abused by customers. If the estate agent in charge of rentals is not pulling their weight then it is unfair on the others.
I agree that the customer is wrong in this situation and perhaps they are just a bad customer, which is an unfortunate reality. About that time is a good time to say "I'll just go and get the property manager for you", then piss off out the back and get someone who is qualified AND PAID to deal with the situation, it shouldnt be your problem.
I sympathise with the customer also though, real estate agents are renowned for being useless self-absorbed twats who couldnt organise themselves out of a paper bag.