Switching hands in Working Equitation is a DQ (disqualification).
Although many levels allow you to use 2 hands on the reins. You must use the same hand throughout the course to handle the obstacles or you will be DQ'd (disqualified) from that trial.
The Switch Cup, may be on the opposite side to your working hand, and even high-level riders in a hurry have been known to make the mistake of reaching up with the closest hand.
One way to remember is to carry a whip in the non-obstacle working hand.
It will remind you that hand is full so you use the other one.
Tell me below how you've been DQ'd for switching hands, or how you make sure you aren't.