One of my unbeloved Schubert Chokecherry Trees is in need of trimming again this spring.

When it was smaller, I left three main branches as it didn't give much privacy without the extra foliage and branches. It's now bigger and I should probably correct the problem I created. (Or just cut the stupid thing down and replace it. That may give me even more headaches as the previous owner planted it quite close to the gas line)

With three main branches shaped like a three pronged fork, I'm asking for trouble, as it causes weakness, correct? The outer two are about 7 inches in diameter. I should cut them completely off this spring and the main trunk will continue to branch out further won't it? Or have I created a narrow tree for myself?