Hi Kevin,
I'll chime in with a few notes since I haven't seen them addressed yet.
First of all, I do patent law so the best I can do is give hints and guesses in the other areas: TM and (C).
You mentioned all 3: patents, trademarks, and copyrights.
Briefly (and grossly over simplified), copyrights prevent direct copying, trademarks prevent consumer confusion resulting from similar branding/packaging/slogans, and patents protect inventions.
If you infringe their patent and it's valid and enforceable, you're out of luck until the patent expires or you sign a license. To find out whether you infringe or whether it's enforceable is very involved and, accordingly, expensive. They should at least identify their patent, however.
If you violate their copyrights, it's probably in your labeling. You can simply change your labeling to get around that. If you quote their labeling for comparison, use quotation marks and give attribution. You shouldn't need permission to critique their language -- an exception known as "fair use."
With respect to trademarks, I suspect your use of "Hydroxycut" is too prominent -- or they're incorrect in their assertions. There's a case I mentioned in this forum a while back in which a generic perfume claimed to smell like "Chanel No.5" (or some other number). They won on the notion that they were using the "Chanel No. 5" trademark to refer to the Chanel No. 5 product, not their own. This was a while back, and I don't know if there have been any new developments in this area. But you seem to be okay (within the law) in comparing your product to Hydroxycut by name. Trademarks aren't supposed to make products impervious to comparison and critique.
I hope that helps.
Regards.