Make sure you are keeping some contact with the reins as well. It looks like she is trying to dodge the contact on the right rein by softening her neck and dropping her head. Make sure that you are the driver and not a passenger when you come into that right cirlce and ride her to where you want her to go.
The leaning around the corners is a sign that she is not that balanced going in. I would agree with SPhorsemanship that school figures, including serpentines and small circles are the way to go.
You could also try a 1/4th arena circle in each corner as you canter through it so you go around the corner as normal, make a full loop and then carry on back on the same path. The smaller circles will force her to balance better, just be sure that you are able to balance as well!
With the reins you can also try even pressure with both reins but pull, release, pull a little harder, release, etc. Eventually horses will learn that the gentle touch with the reins (combined with the other aids) means stop, without you ever having to go to a harder pull. Check the bit too and make sure that it is right for what you are trying to do. If she is already a little hard mouthed then you may want to change to a stronger bit, get her lighter in the hand and then switch back to your original bit once she is listening better.