Hmm, I can’t see why they would conflict. As long as there is no duplication of classes etc, I don’t see what’s wrong.
It would be easier to suggest solutions if you got rid of the iframe. Let us see the page as you’ve tried to build it. This issue has nothing to do with WordPress I suspect.
Hmmm, looks more like a CSS conflict to me. Can you tell what styles are not applying now that were before? It might be work putting up a separate version of the page without the slider, and check each element style in order to see where the differences are.