Yes, mobile browsers are different from desktop browsers. If you're going to design for mobile, then understanding the differences - and coding for them properly - is your responsibility. The HTML export feature in Fireworks is only intended for making prototypes (to check or compare concepts, for instance). It's never been recommended for making live sites.
You'll have to redo your menus in Dreamweaver, preferably with CSS menus that are cross-platform and cross-browser compatible. But you need to understand the requirements, first. And then you need to ensure your code satisfies your requirements. That's why you're the designer/developer and Fireworks is your graphics production tool.
Thanks, great answer.
So the links don't work with one single touch, but do when touched twice. Unfortunately, the double touch has to be just so to make it work.
It is sensitive. Problem is users are use to a single touch on links.