Why do you think showing your other site on your first site will help its rankings? There's nothing to gain by doing this for SEO. Not only is traffic not a ranking factor, but iframes are not SEO friendly so that content is invisible to the search engines anyway.
So this is not useful and could possibly be seen as an attempt to manipulate the search results because that's exactly what it is.
If the other site is having its rankings drop it is almost certainly due to low quality content as this is something that is continuing to play a larger role in Google's efforts to improve its search results. You need to determine why the content is considered low quality and address it accordingly.