OK. It was on different subnets! Problem solved. I reconfigured my secondary router to wireless bridge mode. There's now a slight chance for an IP conflict, but it should be good. Don't ask. My Mom won't let me design her networks in a way that makes sense...

When I flattened it, there was no problems, and the printer was detected immediately. On my laptop, it turned out, it didn't work. Probably something to do with it being so mobile. It doesn't understand how to detect on multiple networks, or something.

Turns out this whole time, it wanted a password for my local user. That's why it wasn't working when I typed it in. For some reason, it looks different than most boxes that ask me for the password for elevated permissions.

I deleted my home printer (I can re-add it later), and had to fiddle with the printer, as it kept choosing an error which said some internal cups error or something. So I had to choose a different protocol, which I can always check later.

In the end though, I had two machines, printing a test page. I think this is good enough for now, unless I come back later and can't add my home printer.