From what I can see, a powered usb hub has an ac adapter to it. Is that correct? And from what you are saying, maybe the printer doesn't work because the port doesn't have enough power, so the powered usb will help that. Is that also correct?
Correct on both counts. Once the hub is powered, any usb device you connect to it will not draw power from the computer.
So I don't have to make a second trip, what do you recommend if:
a. I don't see the printer listed.
b. I do see the printer listed, but I am still unable to recognize the printer in the printer section of my preferences.
The hub itself should be listed in the USB device tree. The printer will be listed as connected to the hub. (The image I posted shows the hierarchy.)
If neither the hub nor the printer show up in the device tree you will have to dig deeper. USB port on the computer? Cable? etc.
If the Mac sees the printer, i.e. it is listed as shown above, you can set it up in the usual way: System Preferences / Printers & Scanners / (plus sign to add a printer) -- the Brother printer will be listed. Select it and proceed.
The ideal situation is to have the printer attached to the main house computer, not the laptops.
Once the main computer sees the printer, other computers that are on the same network as the main computer can share the printer. All you need to do is setup printer sharing. System preferences / Sharing, and check Printer sharing.