Where is the Network printer connected? Is it connected to one of the laptops, or, is it connected to a hub or router on your network? I never had this problem, but, I used to make the mistake of not unchecking the "shared" option on desktops/laptops that didn't have the printer attached to them. Some of the other desktops/laptops, instead of finding the printer on the network, would attach themselves one of the other computers that had "shared" option checked. Which resulted with a printer queue from one computer looking at or adding to the printer queue of one of the other computers where the printer wasn't attached. (Is that confusing? It is to me.)
If your printer is attached to a hub or router, make sure that none of the computers have the "shared" option checked in the printer setup. If your printer is attached to another computer on the network, make sure that computer is the only one that has the "shared" option checked, and see if that helps. If you already set up the printers with the shared option checked, you might have to delete the printer and set it up from scratch on each machine, including the one which has the printer attached to it.
If that doesn't help, wait a bit, and see if anyone else has a different answer. Maybe someone who has already come across the problem of "Printer Gone Wild" (Heh). You never know, folks here have set up a lot of networks and a lot of printers in their day, and might have just seen this problem before.
Edit: Just another thought. Make sure you have the correct printer driver in the setup, or, install the hplip-gui application. I have all HP printers, and sometimes using hplip does a better job than cups.