I agree with your D's voice teacher that sightsinging is very important. The performer who can sightsing well has an edge in auditions where s/he may be called upon to read a new piece for the auditors. A performer who can read music and sightsing well will also be able to learn new songs on his/her own instead of having to rely on a vocal coach or recordings. Recordings won't be available if you're cast in a new show! The great majority of college MT programs require that students take courses in music theory/sightsinging and piano. The goal is to be able to read music, sightsing reasonably well, and have enough skill at the keyboard that they can learn new music on their own.
If your D has the time and sufficient motivation to do this on her own, I'd suggest buying a small keyboard and taking a look at some of the book - CD combos offered at this website:
http://www.singers.com/instructional/sightsinging.html
I am sure that there are other websites offering similar materials. I just did a 10 second search.
You might consider seeing if there is a music teacher in your area who would be willing to work with your D on sightsinging/music reading skills. IMHO it would be easier for your D to learn to read music and to acquire sightsinging basics with help from a live teacher.