It's worth giving it a go. Keep the goings on at the remote end as simple as possible. It's obviously best if you both use the same software, if only for the collaboration side of things - you can always transfer the vocal files to your normal DAW of choice.
So unless she already has the same software as you, you'll need to pick a DAW to use. Cakewalk by Bandlab (previously Sonar) is free, but Windows only. Reaper is a low cost alternative for both Mac and PC. Or you may be able to use the basic DAW software that often comes with recording interfaces.
All you need her to do is record the vocal, so I'd suggest sending her a simple project folder that when she opens it up has a stereo backing track and a lane ready for her to add her voice on. If you want her to do harmonies, or double/triple track the vocals then add lanes for those.
She's going to need some decent sounding closed-back headphones, so she can hear the backing track, and she'll have to learn to ensure that the USB mic is selected correctly as the audio input for the track.
You'll need to visit and find the best spot for recording her vocals - and it might involve getting her to hang some duvets up.
So I'd create a check list of her to do before each session, so that she doesn't forget anything.
What I don't know about are any USB mics that are decent sounding and have provide decent low-latency monitoring built-in. However, I'd imagine that the Rode NT-USB might be a good one to think about. It does have a direct monitoring facility which avoids latency issues (but doesn't allow the user to hear vocals with any reverb added, which can make it easier for the user to sing). http://www.rode.com/microphones/nt-usb
However, that mic has only 16-bit conversion, which means that the signal level will need to be strong (with the danger of overloads on loud sections) to get noise-free recordings. 16-bit may be fairly standard for USB mics to maintain compatibility with tablets etc.
Maybe someone else knows a good USB mic with direct monitoring and 24-bit depth recording ability?