Using HTML exported from a graphics application in your pages is a very VERY bad idea. You see the result. The best approach is to create your graphics in FW, and use DW to build the HTML, not FW. The HTML function in FW is only useful as a way to quickly build a PROTOTYPE page for demonstration purposes, it's not suitable for use on a real web page.
Show us your code and we can fix this for you. Alternatively (and better), just use DW to apply your rollover to this image.
Dreamweaver cs6 has a bug here. It doesn't at a border describtion at rollover pictures, and the internet explorer makes a border automatically, if it isn't defined. You have to go to the source-code and at a > border="0" < at the description of the pic. This is it, have luck (: