Are you suggesting removing the entire double branch trunk on the right or just the far right portion?
I am suggesting the removal of the entire second trunk. This of course is nothing but my opinion which along with a buck and a half might get you a cup of coffee. If you do this make sure that you leave a stub of about an inch. This will keep the scar small, prevent the die back of a large portion of the trunk, possibly, and leave you with the option of creating a jin feature.
This is a nice little Mugo and I am not suggesting anything in a flippant manner about the tree, it is what I would do having faced this decision many times and found myself having to remove what I thought I would have to remove years latter when it became a large issue.
Been looking at the tree some more and think it will look good by removing what you suggested because it will end up giving the trunk more movement, right? this is best done in the spring correct?
To give you some idea by what I mean about cutting a questionable branch earlier rather than latter. This Mugo has been in my possession since 1972 when I found it as a 3 gallon nursery tree. It had some of the same problems your tree has and I failed to deal with it at the time.
So the tree developed and became an almost nice bonsai but it's form was alway less than what it could be. The two main branches always left a feeling of conflict until 2001 I finally got up the nerve to deal with it. Believe me it is a difficult thing to do; drastically redesign a tree that most people think it already a finished bonsai.
The last of the series concerning this Mugo follows below. I let the tree rest for a couple of years then started a redesign program with my original thoughts in mind. The results are a major change and there are a few elements that will take another year to refine..
Have to go hunting for another version, the site did not like the file format. Stayu tuned
I/ve got to search my hard drive for a photo that is not in NEF format, even if I have to take a new photo tomorrow.
Is it possible to open up the image and re-save it with a different format, such as jpg?
It is easy to say something but I think it carries a bit more weight if you can show you have done it, in this case not just a simple reduction of a first stage nursery tree but a major assault on a major piece of material most people would have been happy with.
I posted this after your second round of pictures, but I deleted it to wait until after you finished.
I like it a lot. Was this tree in a pot its whole life? I'm a beginner, so take this with a grain of salt, but I think it would look nice if the apex was moved a tiny bit back towards the center of the tree. I'm more trying to train my eye than anything.