I’d like to perform the change shown in yellow in the two images below but I don’t know how to. 

Select the edge, open the edge menu (Ctrl+E) and use “Rotate edge CCW”
Or you could dissolve the edge and then add an edge with the knife tool.
Ain’t that the change you wanted? (for the opposite side you would use rotate cw instead of ccw (clockwise instead of counter-clockwise)
