If you are trying to plug in both printers at once I presume you are trying to use a USB hub? Not all hubs are compatible.
So test first by plugging the printer directly to the USB port on the Extreme.
Apple's instructions are not particularly helpful.
https://support.apple.com/en-us/HT203159
But it can be a problem caused by the printer being previously plugged into the computer and now plugged in by USB.
Apple recommends you clear all printers before you start.. Then attempt to add the printer.
Some printers simply are not compatible with sharing over a network.
If you can load the printer and it is recognised by the computer as available on the network but still refuses to print, try changing setup so the computer is linked directly to the Airport Extreme and not via another router. This can be crucial where bonjour is not recognised by the main router.
It would help if you described the network.
What is your main router.. make and model??
How is the Extreme connected and in what configuration? Bridge or as router?
Can you get the computer to directly connect to the Extreme if it is using wireless or ethernet from the main router which is NON-APPLE?
It should be possible to directly connect to a printer using IPP method .. I will test this and post back some screenshots if it works.