To connect two Hitec buddy boxes, or a Hitec and a Futaba together, you need a special Hitec Buddy Box cable. Nothing else will work. It's not a straight-through "regular" DIN cable like the one you are using. If you do not use the proper cable, things will not work correctly, the buddy box will transmit (bad) and I have heard stories where one of the boxes actually started to smoke!!!

If you can control the plane without the buddy cord attached, then it's the buddy cord that is the problem.

The proper operation of a buddy box system is this: Master box, the one that would control the plane if you were flying solo, is held by the instructor. Buddy box does not transmit at all, and should not transmit, because if you're transmitting on a different channel, you can shoot someone down, and if you're transmitting on your own channel, you'll shoot yourself down Anyway, the instructor holds the "dead man's" trainer switch on the Master box, and can let go on a moment's notice, when the student gets into trouble that he can't recover from.

Anyway, the best course of action is to get that Hitec buddy cord before you go any further.