Problem accessing hard drive for more than one user at the same time

Question

Hello all,
I recently bought a 2nd generation AirPort Extreeme 802.11n to replace a cheapo wireless router. The main reason I wanted to get the AirPort was so I could attach a USB hard drive which holds iTunes music files Originaly I had a G4 MDD and this was a second internal hard drive. Since my wife and son also share my Mac, we stored the iTunes music folder there, so we could all access the files. That worked fine.
Then I got a early 2009 iMac and gave my wife the G4. My son also has a G3 iBook, using the wireless internet conection. At first I had the drive in an external case attached via Firewire. Both my iMac and my wife's G4 are attached to the network using ethernet, not wireless. She was able to access the music files so long as my Mac was on, but the connection was flaky.
So as mentioned, I picked up a used AirPort Extreme from OWC, mainly to attach the hard drive, since it's no longer in my Mac. It took some fiddling, and I was honestly surpsied that the APE was trickier to set up than expected, but now I have the external drive mounting, and we can all access the files from any of the Macs in the house. It works great except for one thing. If I'm logged into my iMac, and then another family member logs in on the same iMac, we don't all have access to the hard drive. It's still mounted, but the you have no permission to view the files on it.
Then if I remount it, I can access the files, but now the other user can't.
So in a nutshell, only one user can access the drive at the same time from the iMac, but we can all access it from different Macs.
Anyone have an idea of why this is happening and how to remidy it?

Answer 1

This is the boilerplate text often used in connection to saving to a network (please NOTE the part where it explains that normally, it does work, but that it is impossible to troubleshoot someone else's network remotely, and that's why it's not supported by Adobe):
If you are opening files over a network or saving them to a network server, please cease and desist immediately in the event you are currently experiencing problems with one or more files. Working across a network is not supported.
See: 
http://kb2.adobe.com/cps/406/kb406793.html
  Copy the CLOSED file from your server to your local hard disk, work on it, save it again to your local hard disk, close it, and copy the closed file back to the server.
     Of course, the fact that Adobe does not support working across a network does not necessarily mean it won't work.   It should.
    Adobe's position is that there are too many variables in a network environment for them to guarantee that everything will work correctly in every network, especially given the fact that if something does not work properly, it's probably the network's fault, and Adobe has no way of troubleshooting your network.
  If you can't work locally, you are on your own, and if something happens, you're on your own. If you must work from a server, make sure your network administrator is a competent professional.
When problems arise, a lot of valuable work can be lost.