Docking the TST window on the right side of the parent Firefox window has been added in version 5.3 of the extension and is available as a setting on the options page. It is under the "Docked Window Settings" section in the "Open beside current window" area and is called "Open the window to the right of the main window instead of to the left".

This extension relies on Tree Style Tab's "sidebar" page being robust enough to work correctly when there are several such pages open for a single window. This was the case when I initially developed this extension but later changes to Tree Style Tab broke that behavior. Fortunately Tree Style Tab's developer is quite friendly and made some changes that makes this extension work much better again. These changes were released in Tree Style Tab v3.5.7. So if you have that version or a later one then hopefully all of your issues should be fixed.