So how is your instructor teaching you to strike with the rear hand? It's not uncommon for some schools to teach a quarter-turn rotation to a vertical strike for a rear hand strike, but both are acceptable, and both are still legitimate Hapkido.
Hapkido is based on one general and three specific principles which combine to make it a unique art. The general principle is known as UM-YANG and is similar to the Chinese concept of Yin-Yang. The principle of UM-YANG is reflected of the opposites which make up our world. In Hapkido opposites are represented by the way that you respond to an opponent's attack. Depending on the situation, you could respond with softer, more circular UM techniques, or you could choose to employ harder, more linear YANG techniques. More often than not both aspects are combined in a response, such as circular blocking combined with linear striking. This general philosophy is combined with three specific principles: HWA, the principle of non-resistance, is the act of not directly opposing your opponent's strength; WON, the principle of circular motion, entails using a natural, free-flowing, circular motion to add your opponent's energy to your own; and YU, the water principle, the act of surrounding and penetrating your opponent with techniques.
Don't discount the importance of linear movement in Hapkido. The beauty of this art is it's ability to flow between circular and linear motion. The indirect strength of employing circular motion for direction is complimented by the direct strength of linear movement for penetration. Without a proper appreciation for both you are limiting your options and are only getting a part of the art.
Happy Training!
Bill
I didn't even get a chuckle out of that one. 
