Airport will connect to Brother 2270DW via USB but not ethernet

You have gone into Printers And Scanners in system preferences and added the printer?

It's important to understand that when you connect a printer to the AirPort's USB port, the base station's print server is enabled and used to share the printer with the network. However, when you connect a printer to the base station's Ethernet port or by Wi-Fi, the printer itself must provide this service. In the latter case, the base station does NOT detect the printer other than it keeps track of its MAC ID address. The base station does NOT recognize that it is a printer, just another network client and assigns it an IP address like any other client.

So, when connected by Ethernet, the printer must be recognized by the network client that needs to use it as a resource. That would mean, that client must have the latest printer driver for this printer that support network printing.

A following things may help:

• Assign a static private IP address to the printer. This should help network clients "find" it easier.
• If your printer support Bonjour, install Bonjour for Windows on her computer.
• If your wireless network using a Network Name (aka SSID) that includes spaces or special characters, rename it not to use either. For example, if your current wireless network is called: M% WiR3less *etwO#k, rename it to something like: MyWirelessNetwork
• Finally do not use the "hidden network" option as a security feature.