Very good posts above. You are are very unbalanced in the saddle, which will make it much harder for your mare to keep herself balanced upright and off the forehand.
As the above posters said, sit back on your seat bones more, so that you have a 'triangle' or contact on the saddle. Your two seat bones, and you pubic bone, should have your weight evenly distributer over them.
Keep your shoulders back and then really work on relaxing your thigh/knee to allow the lower leg to come more under your centre of gravity and stabilise to become more effective. At the moment the lower leg is almost totally ineffective and is just 'waving in the wind' so to speak. You really need to loosen that upper leg to get a steady lower leg, I'm sure you will find that she is much more responsive once you make this change ;)
Our upper body's carry the bulk of our weight, and so when you are leaning forward and tipping onto your pubic bone, you are inadvertently pushing weight down onto the horses shoulders, which in turn creates a horse that is on the forehand. It is very difficult for a horse to come off the forehand and begin to come over its back when the rider is pressing their weight onto it's shoulders.
Your mare is a VERY good horse as she's not falling on her face. So once you can get yourself into an upright, balanced position, just imagine how much nicer she will be
Your trot also seems to fall apart a bit after the canter. This is because in canter she is not going forwards at all, and you are blocking her through your pelvis, so when she comes back to trot she is already unbalanced and on the forehand.
I recommend that you do millions of trot-canter-trot transitions once you've fixed your position, in order to get her hind legs more active and really working her back muscles. In canter, try to ride 'into' her rather than just sitting on top of her. If you can picture your seat being connected to her, think that your seat is your accelerator and brake rolled into one. Push into her to stay with her movement and have control of it. You need to be in control of the speed of the canter by using your seat, so really try to sit into her and drive rather than being a passenger and having nothing but rein to try and steady her.