[pip08456]

Don't worry General, this guy's been here before.

@beaker 17. Here's what happens with your printer and your home network.

PC - router (wired connection) router - printer (wireless connection). Everything in the home network goes via the router (or hub) and the connection is made by the router by whatever means the device uses.
So, the computer (PC) wants to print a document, it asks the router to pass the request to the printer. The router knows the printer is connected wireless so sends s signal to it with the request.
The printer responds and says "yes I'm ready and willing to do that send the request over, I'll do it."
Your router then responds to your PC saying the printer's ready send me the document and I'll pass it on to the printer.
Your document is printed.

Your printer is connected to your PC via the router and not by your "all in one" wireless PC.

When you connect a PC, laptop or whatever via an ethernet able it automatically disables the wireless connection. Your device will always choose the fastest available connection.

Disconnect the ethernet and your device will automatically search for a wireless connection.