I'm new to the game and just got a H.O.T.A.S. - so I re-did the training module for docking and travel in 3.3 Beta... and there appears to be a bug with the hyperspace travel. You just get stuck in the jump, and it never arrives at the location. Tried twice now, and only way out is to end the task of the game. I targeted Eranin as instructed and jumped to hypercruise, and i'm just... cruising... with no end in site. after about 10 minutes, i call it quits. Might want to check it out, or let me know what i did wrong.
I don't know how long you have been playing but if I understand your issue correctly, you are jumping from normal space to supercruise. Supercruise is an intersystem travel mechanism. To jump to another system, you need to hyperspace there. Hyperspace travel is distinctive in which you will not be able to control the ship. If you are able to control the ship immediately after a jump, you are in supercruise.
It is not my place to tell you how to play but I would advise you to stay away from the beta for the moment as it being a beta, it needs bug fixes and can spoil the experience for you. Stick to the live version for better stability. Also, this is not the correct thread and I would advise you to post any questions in dedicated parts of the forum.
Lastly, this game is one of its kind. Experience it, feel it, and you will sink hours in it.