Playing left-handed: do you get relief?

As a right-handed player, you normally play right-handed. But if your ball lies where that is not possible, you play left-handed instead. Whether you then get free relief from an immovable obstruction is covered by Rule 16.1a(3) and two Clarifications.

When the lie calls for the stroke

Your ball lies right next to a boundary fence. There is no relief from the fence itself, as it marks out of bounds. You cannot play the ball right-handed here, so you play left-handed. If you are standing on a sprinkler head as you do, it interferes with your stance and you get free relief. In these circumstances, the left-handed stroke is not clearly unreasonable (Clarification 16.1a(3)/1).

Drop, then right-handed again

You drop within one club-length of the nearest point of complete relief, not nearer the hole. You find that point for the left-handed stroke. After that, you may play right-handed again. If the sprinkler head then interferes with your right-handed stroke, you may take relief again for that stroke or play the ball as it lies.

When it is just a trick

It is different if your ball lies badly and nothing interferes with a right-handed stroke. If you set up left-handed only so that the sprinkler head interferes, you get no relief: a stroke you choose only to get relief is clearly unreasonable (Clarification 16.1a(3)/2). You play the ball as it lies or take unplayable ball relief for one penalty stroke. The same applies to a stance, direction of play or club that you choose only for that reason.