Printing Connectivity with my Modem
You haven't specified your Brother printer, but there is a known issue that affects how some of Brother's printers communicate with macOS systems. When I say it's a known issue, you'll be hard pressed to find it documented in writing, although you will have this confirmed if you get the right Brother support person on the phone.

There are some workarounds you can try, but these are not guaranteed to work 100% of the time. The only option I've found that will work 100% of the time (based on my experience with a limited number of networks using Brother printers), is to disable IGMP snooping. However, if your modem/router does not provide configuration settings for IGMP, then you'll have to purchase one that does.

So, your options are:


Disable IGMP snooping if your modem/router supports this
Try connecting to the Brother printer using CUPS (i.e. do not use AirPrint when you add the printer to macOS)
Use your modem/router to allocate a static IP address to the printer (using the printer's MAC Address1 to identify it) and also configuring the printer's network settings to give it the IP address you've set at the modem/router end
Connect the printer via USB cable instead of Wi-Fi to your MBP when printing


If you still get no joy, then your best bet (assuming you want to keep using the Brother printer) is to purchase a modem/router that supports IGMP and ensure you disable IGMP snooping.

Regardless of what you opt for, I strongly suggest you actually reset the printing system on your MBP before trying each of the above options. To do this:


Got to Apple > System Preferences
Click on the Printers &amp; Scanners preference pane
Right-click on the list of printers on the left-hand side and select Reset printing system... 
At the next prompt, click on the Reset button


Remember: Make sure when you add the printer back that you use the CUPS option and not the AirPrint option. (Don't worry, you should still be able to print to your Brother printer from your iPhone and iPad).

1Not to be confused with your Mac computer. See MAC address for more info. You can obtain your printer's MAC address from its configuration menu.