I notice in your screenshots that you have both files in both directories. Having 11291s01.dat in the parts directory is presumably why you see the "just right side" subpart in Bricksmith's parts list. Since you do have it in parts/s also, I don't know why the 11291 isn't showing the whole part.
There is one other thing you might try. First, delete all 11291*.dat files from your ldraw/parts folder. Next, open a file that uses 11291.dat in LDView. LDView will automatically download the needed files into ldraw/Unofficial, and put them in the correct locations. I believe that Bricksmith will then see them.
If you don't know how to create a file using 11291, put the following line in a text file, and save it with a .ldr file extension:
1 1 0 0 0 1 0 0 0 1 0 0 0 1 11291.dat
There is one other thing you might try. First, delete all 11291*.dat files from your ldraw/parts folder. Next, open a file that uses 11291.dat in LDView. LDView will automatically download the needed files into ldraw/Unofficial, and put them in the correct locations. I believe that Bricksmith will then see them.
If you don't know how to create a file using 11291, put the following line in a text file, and save it with a .ldr file extension:
1 1 0 0 0 1 0 0 0 1 0 0 0 1 11291.dat