Jay,
I obtained a Cork Bark Chinese Elm last year. Similarly it also had two trunks but on mine it was higher up. The first thing I did was to cut it off after selecting the one to keep with the best taper. It was then potted in a deeper training pot and allowed to grow through the summer. It rewarded me with a profusion of new growth all over the tree. These have now been selectively pruned and wired and it is now in a new training pot. I am waiting for some photos. When I receive them I will post them so you can see. Personally having been in a similar situation, I would remove the trunk with less taper and let it throw out new shoots (which in my case they came from everywhere) and over time it will give you a much better shape. This is just my advice, you have to look at it every day, so do what you feel comfortable with, and Earl is right you can't put it back on once it is cut off.
Ant (photos to follow)
