As you noted, copy and paste from you laptop to the external drive does not move the files, it just copies them. If you want to move them, use Cut and Paste, or copy and paste, then delete them from the laptop.
Do you keep the external drive connected to the laptop all the time? Do you want to move some of your data files to it and work from it rather than your C drive when adding new files or editing exsiting files? For example, you could actually move your My Documents folder to the external drive.
The major problem here seems to be your procedure for copying files from the other computer(s). Going through AIM is not the best way to do it; I'd say it's a bad way to do it. Do you have the computers actually networked? If not, I believe you need to focus on getting them networked and setting up file sharing. Then, you should be able to mark that external drive as "shared", thereby giving it direct access to the other computer(s). I could be wrong, but I'm fairly sure this will stop the intermediate copying of files to your laptop when you want to copy/move files from computers other than the laptop to the external drive.
To reiterate, networking and file sharing is a solution. Also, if you're using the external drive mainly as a backup device, you could connect it directly to other computers as long as they have a USB port available.
