Hi Varuza! There are some good explanations of which muscles are used in belly dance on the Bellydance for Body Shaping series by World Dance New York. The explanations are provided by a personal trainer, and the screen shows muscle diagrams to illustrate the points.
Suzanna Del Vecchio's Precision Motion Workout might be something you'd enjoy. She is very anatomy aware and provides crisp explanations in technique. The video contains an hour of study/instruction/technique, followed by a 30-minute drill session which could be done by itself as a workout if you insert your own warmup in front of it.
If you want something more elementary than Suzanna's video, you might like Joyous Laughter, Volume 1: Belly Dance Basics with Michele. That one begins with a well-described study in technique, followed by an 18-minute drill/practice session.
All of these are reviewed in detail on my web site. The World Dance New York ones are at
Belly Dancing: Shira's Reviews of Fitness Videos and the other two are at
Belly Dancing: Shira's Reviews of Instructional Videos, Alphabetical List
I hope this helps!
--Shira
PS: If you like Core Fitness well enough to keep it, then I do recommend contacting World Dance New York directly to explain your problem and see whether they'll agree to an exchange.