Hello Jim. Thanks, and welcome.
The urination scene has been mentioned a number of times previously, but to my knowledge, there has been no discussion as to why this scene was not included.
A month ago, I think I did make some personal notes on the scenes in the story that were NOT included. This scene and the dream sequences are the most prominent. (There is already a thread dealing with the dream sequences and what possible effect their omission had.)
One thing that came out of my notes is that Ang Lee's style would probably have dictated the exclusion of such scenes. His style in this movie is very understated. He reminds me of a bonsai tender who prunes more than anything else. The sensibility pertaining to this scene would have been much too vivid (and brutal) for his taste, I would say. Plus, it would have been difficult to link this to the other scenes cinematically speaking. As a part of the short story, it makes brilliant sense -- acting as a commentary that brings to life the already deceased Jack, as a device that throws into sharper focus Jack's troubled relationship with his dad, and as a barometer to Ennis' darkening horizons close to the end of the story.
Also, note precisely where in the short story this recollection by Ennis is inserted in. It would have been awkward in the movie to include it there, and it would probably not have made that much sense to include it in earlier scenes. The movie loses a bit of the emotional precision this scene gave, but gained in subtlety. Everything was already implied when you get to see John Twist during Ennis's visit to Jack's boyhood home. Plus, the movie makes reference to visual signposts (in this case, 'American Gothic', by the painter Grant Wood) -- something that was not done in the short story. Some gains, some losses...