Elizabeth,
I have never had tendinitis of the hip but I have had some in my knee, from dancing, and the elbow and shoulder from working out otherwise (or dancing with a really rough partern

). For tendinitis to get better, follow these three steps.
Rest : Lots of it. Staying off your hips might help . If you have to be on them, restrict your cuban action to just the dance floor.. Ice: Ice the joints often. Alternate heat and ice relieves pain well too.
NSAIDs: Anti-inflammatory drugs, work great for pain as well as inflammation. You can take upto 800 mg thrice a day (with food) and not have a problem - unless you have ulcers or are otherwise affected by it.
I guess there is a fourth option. Work out and strengthen the pelvic muscles. Although for that, you must seek a personal trainer or a sport-medicinist, I don't know what exercises help.
Although half facetious, those were the tips I was given. I hope they help.
Get well soon.
Sri.