Printer sharing in Windows 2000

I have 12 computers on my LAN that are dedicated to training. Each computer is running Windows 2000 and eight of them have printers attached as local printers on LPT1. The printers are of mixed manufacturer and models. There are two login accounts on each computer, "Administrator" and "User".
In order to conserve space and make more efficient use of the printers, I would like to share one printer with two computers.
With the printer on the local computer set up as a share (hand underneath):
1. I log-on the remote computer as "Administrator" and can go through installation of a local printer using the Printer Wizard (create a new port, enter \\computer_name\printer_name, and designating this as the default printer). I can then log-out and back in, shutdown/restart, etc. and the printer remains as the default and is connected (can print without taking any additional steps).
2. When I log-on the remote computer as "User" and follow the same steps, I CANNOT install the printer as outlined above. I must do a search for the local computer, sign-on as administrator, connect the printer, and set it as the default. It then works as desired until I log-off, reboot, etc. Once I reboot and sign-on as "User" again the designated printer IS shown in the Printers Folder as the default, but it is not connected (I cannot print to it until I go through the search, administrative sign-on, and connect routine again).
I desire to have the printer be the default printer when I log on to the remote computer as "User", and available without having to go through the administrative sign on and connect routine each time. Where am I going wrong?