Hi Rachel,
Unless you have some specific reason you want to integrate the directory with the cart, they would act independently of each other. They create different types of pages with their own php files.
WordPress plugins are designed to work with whatever theme you are using. You shouldn't need to worry about the theme being compatible.
Have you run into a specific problem getting them to work together?
I don't have a specific recommendation, but we did have a tutorial on this topic you can look at.
www.ostraining.com/blog/wordpress/quick-...directoryphone-book/ Let us know if this helps.
Cheers,
Ed