It's called "Right Seat Dependancy" training at one FAR 121 airline where I used to work. Besides the usual sim scenairos stated in some of the posts above, we were required to perform 3 actual TOL's in the A/C from the RHS with a check airman in the LHS every 12 months.
Normally, the Captain in the RHS was the PNF, with seat swapping the norm with the Commander.
In my experience, most Captains assigned to fly a trip in the RHS, whether senior to the Commander or not, welcomed the opportunity to relax rather than "supervise" a newly minted F/O.
A real Captain usually doesn't have the ego thinking flying the RHS is beneath him...and besides, seat swapping means moving all of your sh!t from one side of the cockpit to the other...not really worth the bother IMHO....