This can be a "mare" thing but I have more questions. Does she do this in the round pen with no tack on? If the answer is no then you have an equipment issue (or her accepting the cinch or girth issue).
If she is doing it w/o tack and no rider, you might want to check her back AND have her checked rectally for cystic ovaries.
If all checks out physically and it is the same with or without tack, then you know it is a 'tude issue (or could be). In the round pen or lunging, get out the whip. When you want her to pick up the pace, don't ASK nicely, DEMAND it and back it up with the lunge whip. IOW's get her mind off of resisting and on MOVING FORWARD. A horse cannot snake and all the rest of this nonsencse if she is committed to moving forward. If she snakes her head and pins her ears, use the whip a second time and do not hesitate to make her think about it (do not beat the horse, but a crack with it really near her flank can be VERY effective!). If she throws her head up and looks worried and hollows her back but jumps forward, GREAT! Back off a bit and let her go. She needs to understand a request to go forward measn go forward and there is no fooling around. Be consistant until yu can ask her to change gaits and she jumps forward without the drama of snaking heads and pinning ears. You can get her back to working collected as she advances.
Same thing on her back. Use what ever means necessary to get her thinking about forward and not about resisting and be prepared for some bad behavior.
As to backing.. this is really an advanced maneuver. What you need is to first be able to get the horse between your lags and seat and your hands. You need to actually feel you have the ability to drive the horse into your hands tand then beable to LIFT her front end with a half halt. When you can get this, teach her to move away from your leg behind the girth (turn on the forehand). I actually do this at a hitching rail.. where the horse's chest is against the rail and the horse cannot go forward. Use a left rein lightly so you can see her left eye a bit (squeeze and release) and left leg behind the girth to move her butt over to the right.. right leg on the girth to steady her front. Get her responding and doing the TOF in both directions. Next get her off the hitching rail and do this.
When you have these two things going for you, your start to teach the rein back.
I push the horse forward into my hands and resist.. not allowing the horse to go forward. You will feel the horse between your hands and your legs.. and the horse is being pushed forward into your hands and cannot go forward because you are resisting.. so the horse has one place to go.. BACK. If the horse starts to rear (some do), get off and teach it using long lines.
That being said, all the horses I started were driven all over creation on long lines for weeks before I ever rode them. In that process I did train a rein back so they knew they COULD back up. Some horses do not think they can back up so they will try to rear a little.. even on long lines.. just go back to a halter and lead and show them they CAN back up. Some horses.. the first time they find they can back up.. it is like an epiphany.. they start to blink and you can see the old light buld came on. It is pretty amusing.
I forgot to say.. you can keep her straight when she backs using your legs because she has learned the turn on the forehand maneuver. Her job is to back up and yours is to steer.. just like a car. LOL