Yes, that is how it is supposed to be done.
The important thing is that there are two torrents listed in your client as you say "… opened it in uTorrent so it made a new torrent. ..." and "... Now I have 2 torrents pointing at the same file ...". Then each tracker will get upload/download information from the client separately.
If the client wants to add the other tracker (announce URL) to the already existing torrent, because both torrents got the same hash, don't do it. This is good for public torrents only, not for private tracker torrents. The client will mix up uploads and downloads from and to both trackers peers and therefore the ratio etc on both trackers. This might get you banned on private trackers.
If both trackers torrents got the same hash, you could run two different clients, e.g. µTorrent and qBittorrent, or two instances of µTorrent (it is described on their site how to do that) with in each one of the two torrents.
