Pulling content from one site to my wordpress site

It is probably pulling all the HTML from the source but the paths to the images and stylesheets may be relative and so your browser will fail to find those same files on your domain.

First, verify the image and style paths in the HTML that is being fetched by wrapping the whole shortcode in a textarea tag so you can read the captured output.

Then you can experiment with some find and replace parameters to make those paths into absolute links that point to the source domain.