Obviously rule out any pain first up – Teeth, Chiro, Saddle fit, etc.
1) I can't brush her legs, because she picks them up like she expects me to pick them out. It's driving me nuts because her legs are filthy. If I ignore it, she paws at me, and if I continue to ignore it she will turn and bite.
Make sure you have a clear signal for when you DO want her to pick her feet up. My signal is tapping the knee and clicking my tongue. It can be anything you want – Squeezing the chestnut, tugging the feathers, etc. I find it is clearer if you have a voice cue also, and eventually you can just use the voice cue. You need to sue your cues EVERY time you want her to pick up a foot.
When brushing or anything else and she gives you a foot without being cued, DON’T STOP TOUCHING THE LEG. You can stop whatever action you are doing, but you must keep the pressure on, or she will learn that giving you the foot was correct. I will often add in a stern but not angry NO or Uh Uh. As soon as the foot goes back down, release, give praise, then continue on.
If she goes to bite, simply put your hand, brush, or elbow in the way of her head. Don’t whack, just block. I also give a growly AH. As soon as it’s done, forgive and forget.
2) I can't get her to pivot when I'm on her back. On the ground I can make her pivot three steps at the most (On her haunches) by pressing with my fingertips. I tried reinforcing with my reins but she pulls against me.
I’m guessing you mean a turn on the backhand/haunches? Front end moving around the rear?
If so – can you do a turn on the forehand? (Pivoting around the front feet?) Can you move her Shoulder, Ribcage and Haunches independently on the ground? Both of these are pre-requisites for a turn on the haunches. Start with being able to move each zone of her body independently – Shoulder, ribcage, haunches. In the saddle, you can get a helper to apply the usual cue in conjunction with the leg cue to help her understand. Then you wean them off the ground cue to only the leg cue.
Once you can do that – start with the turn on the forehand, as it is much easier! You can do it with the horses head in a corner at first to block forward movement. Make sure you don’t have too little or too much contact with the reins – And make sure you give an open rein so her shoulder has somewhere to move freely into.
Once she can do a turn on the forehand, then you can teach the turn on the haunches. The open rein is even more important here – that shoulder MUST have somewhere to move to otherwise she is blocked and will resist.
Don’t forget to reward the try – A shift of weight at the start, then up to a step, then two, and build from there.
3) Her hind is incredibly sensitive. If I even take a step toward her hind she will move it away. I have to be really sneaky to get near her hind, and when I do she threatens to kick. She'll pin her ears and swat with her tail.
Firstly – Stick close to that butt if she threatens to kick. If you are nice and close, the worst she can do with a kick is give you a shove. If there is distance – She can get you a good one. I would move toward her hind with a hand on her back at all times. If she moves, just stick with her. She may circle a few times, but once she stops, praise and rub with the hand on her back. Leave it at that for a session. Each session, stay near her butt for longer, If she swishes her tail and threatens to kick, stay close and keep the hand there, then when she stops, praise, rub, and move away.
4) When I'm riding and try to steeer to the right she will rear and turn left. If I insist on it, she will begin to crowhop.
Are you pulling back with your rein or opening it into a directing rein? Can you flex her laterally to your leg on both sides? Make sure you can – She needs to give her head and neck to the rein both sides without resistance.
When you ask for the turn, don’t pull back – Give a big, exaggerated open rein. If she feels like she will rear, push her forward. Keep that rein steady and constant no matter how she evades – The second she gives her neck and takes a step, release and pat/praise.
Small steps :]
5) If I am asking her to back up she will throw her head around and pin her ears.
Can you back her up from the ground? How do you ask for the back up? When I start a young horse, I teach the back up from the bit on the ground before I get on. Then I start cueing with the bit – Gently at first, and rewarding any try. As they get it, I ask for more steps, and I pre-empt the rein cue with my seat. Eventually I wean them off the rein cue and can ask solely with my seat. If she gets stuck, walk forward, stop, then try again.