I think that's a really nice tree. It has lots of potential. I'm not aware of a rule that states 'only one trunk' though. My own favourite tree has three (it used to have five).
Your azalea is almost telling you what it wants to do. If it were mine (which I'm painfully aware it isn't
) I would take out the dead branch entirely and also the the branch to the left (in the picture on the right). The rest will fill itself in over two or three years.
I think it was a very good find!