Our RHS checks consist of EFATO, OEI go around, OEI approach and landing, an RTO and evacuation. There are no requirements for any extra LVO procedures as the LHS pilot is always PF for that.
We have had periods in the past where some captains were RHS checked, particularly in smaller, remote bases where it would be difficult to bring in cover from another base. Nowadays though, I think it is only for trainers.