When a user comes to the site at http://www.****.com/site/mypage as a mobile user, we would like the page http://www.****.com/site/mobile/mypage to display.page.
does this mean you physically have 2 sites? or at least a set of mobile version pages under /mobile/? if that is the case you need a redirect and don't worry about segmentation since you already created a full mobile ready pages. If you were working with one set of pages with logic to render different things depending on a segment, then it makes sense to look into segmentation. but if you already created a mobile version in a separate file then it is just redirect.