Have you got Printer Sharing turned on in both machines in the Network and Sharing Centre (Windows)?
Try activating Windows File Sharing protocol in Firewall > Settings > Ports and System Services
In there you could also open (stealth) a port if HP recommends it.
It might be better if you contacted Technical Support on this as they are more knowledgeable than I. It's free by phone or online chat.
You'd do that on the wife's machine of course. It's linked under Useful Links at the top of this page.
Thanks. After I posted the question, my computer lost access to the printer. I said, "That's It" and took the darn thing back to the store and got a refund. They were pleasant about it even though they had not idea what I was talking about.
That's a shame. Next time, if there is one, Technical Support will be glad to help they are available by phone or online chat for free and linked under Useful Links at the top of this page.