2. My sweetie has been ridden and lunged in short side reins. When I took her last year, I gave up on the side reins when riding and made the side reins longer. The conclusion was utter excitement of being able to lift her neck and look whichever way whilst training... I did not really care about that, but rather waited for her to check that by seeking the contact, our communication is going to be a lot easier and quieter. When lunging, I was basically pushing her forward, encouraging her to rebalance herself by seeking the contact. Ever since, really nice lunge work and a very relaxed horse. As for riding, it was trickier: as the contact line had always been to her sides (towards shoulder/elbow), having a raised line, to the withers, was putting problems. So I started riding with a lowered hand (around the sides of the scapula). It took around a month to understand what "that idiot up there wants", but now, everything works perfectly and I will soon start working on "lifting" her.
Reminder: promptly applied positive reinforcement is enough for your horse to understand the exercise. I always have a whip with me, but never used it as a punishing device for the past few years even if the "pupil" misbehaved. I felt it on my own, that the voice is a better aid than anything else, no matter what. Always have mixed treats, so that the reward varies in 'intensity'. This way, your horse is going to be more motivated to work well to get his favorite treat (which comes by chance - facebook uses the same principle on you ;) ).
And... PATIENCE! It might take a month, it might take several of them...
I would first make sure that I do not ride my horse with my hands but with my legs and seat. It is usually the most common problem. Check if your hands are steady and do not yank your partner's mouth every time you move.
If it is not the case, I had several situations, on of them I personally pay for every month (and is the only thing I like spending money on!):
1. Your horse had been ridden in a manner that left marks (physical or psychological - if 1st case, Hannah alker gave you the answer). If your horse has memories of a bad experience, he may find that raising his head and leaning on your hand is a good idea to evade your aids. Try to comfort him with your voice and ride him with assisting hands ("loose" to nearly non-existing contact) rather than aiding hands. It basically means to just encourage him to go forward and seek your contact. I had such a horse to correct last year. He found that missing the contact is really funny, so he started looking for more and more contact and reinforcement. By the end of the first week he had given up on raising his head. By the end of the first month he had a totally different approach to riding and two months later he was reliable in seeking the contact on his own.
Before anything else make sure her teeth are done and get a chiropractor out. I can't tell you how many times a horse is hurting with their back or teeth. Their backs get pushed out all the time and it's important for us to get them fixed. If both of those are finished and she is still not performing how you would like try throwing some draw reins in her for a few rides. This will help her understand where she needs to keep herself during the ride. Just make sure you use them properly as they are easily misused! Hope this helps! :)
Try sitting up and keeping your hands up. You can also try doing some dressage training.