A couple of possibilities:
A. (I just did this one) If you have the "old" United app on your iPad, plug into iTunes, back it up. Then (while NOT plugged into iTunes) delete the current app on your iPhone. Plug the iPhone into iTunes and then find the United app that is there from your iPad (the icon should look like the old one). Mark it to install. Sync iPhone. Old app back
B.
Goalie also mentions a way to get back the old FlyerTalk app (before up[sic!!!]grade that preceded the downgrade [sigh] and maybe this method would work for some with the UA app.