You’re on a hiding to nothing using workgroups to access shared resources. If you don’t have the resources to set up a domain think about getting a network ready printer or USB-to-Cat5 print server and map the printer via this.
That way the printer is independant of any individual PC and any issues a PC has with the printer will not effect the group as a whole.
If you go though another PC to connect to the printer you name it and it can get in the way.
If your looking for a short fix look into the win7’s homegroup settings as the printer will be a resources controlled by this if its shared.