Why does Airplay misrecognize my computer as speakers?

At work/school, we use the Reflector app and a D-Link Wireless AC Dual Band USB Adapter to allow mirroring from iPads onto the computer screen. Normally, when using Airplay in these classrooms the computer with Reflector turned on will show up as an option for Airplay like below:

On the four iPads that are recognizing the computers as speakers, it looks like this:

They all have iOS 9.0.2. and the D-Link and the iPads are on the same WiFi. I've also tried reinstalling iTunes and Reflector and restoring the iPads. The problem seems to originate from the iPads themselves, not the PC's or their iTunes programs. All the settings look the same but I did notice a difference in the availability of home sharing in the general settings on the iPad.

On the malfunctioning iPads the menu's look like this:

Even when turned on off it still doesn't work:

On the iPads that display Airplay the way I want it the home sharing option is not available:

I've been troubleshooting this for over two weeks now and I would greatly appreciate any help.