The computers having the same name seemed instinctively wrong. I deleted the printer from the remote. Changed both computer names by adding 1 or 2. Changed the work-group to a new name, but made sure the printer '1' was up and running first.
Rebooted second machine.
Searched for HP 4 to install or the work-group and it popped up showing number 2 computer and the printer, and presto. Just can't remember having to do all this before. In fact, I'm sure I didn't.
.