I've had good luck with the Edimax adapter (though not in Access Point mode), and have used a couple rather generic RT5370 adapters that all worked as well, and worked great in AP mode too....
I did, however, have a HM that was originally running an Edimax fail to recognize a RT5370 when I plugged it in (and was showing all 0's for MAC address etc). I unplugged alll USB dongles and removed all the "radio"s from the WIFI tab and everything associated with WiFi from the INTERFACES tab, and also installed the latest Linkmeter package available at the time. Then I reboot with only the RT5370 connected and got it working in pretty short order, but I don't recall exactly which of these actions did the trick...
Are you sure there isn't a MAC filter in place on the router that is blocking connection by device? That would be one reason why only the one adapter that is already connected will work. If I were you I would remove all WiFi dongles, use a LAN cable to connect and clear out all radios from the WIFI section, then clear out all wireless related Interfaces, then power down the rPi. Now temporarily disable all security on your WiFi router and boot up the HM with the RT5370 connected. Watch for IP on the LCD, most likely you will see the IP of the wired LAN adapter, connect to the HM on that IP and go through the steps to setup the WIFI connection and hope you get through, then re-enable WiFi security.