Can I ask a question first? Is your mare quite tense? Does she tense up when you try and use the reins?
Because if she does, then she sounds exactly like my mare. I would suggest a couple of things which have worked for me and my excitable mare. If you have a lunge ring, lunge her a little before you ride, but its not a neccessity (I don't do this). Then I would take her into a safe, confined area and start with a walk. I walk my mare around, ask for lots of change of directions, circles, figure of eights etc. and ask her to keep at a walk. I don't get mad at her, I just simply correct her each time she tries to go faster or doesnt want to go in the direction I asked. My mare usually is very hyped up at the beginning, jogging sideways etc. but eventually she calms down as she realises that life is easier if she simply does as I ask.
Then I moved on to a trot. My mare is VERY sensitive to the leg and its hypes her up so in the beginning I simply used a voice aid as it calmed her down, made the trot a little slower. At first I asked her to trot for only a few strides then back to a walk. I did this a million times until she didnt rush forwards. Then once she was doing that calmly, we moved on to trotting circles. Boy did my mare want to trot SO FAST! So I used voice aids again (a good woah or a wistle, whatever calms your mare down), squeezed with my thighs and slowed down my rising trot (I find that the best way for me was to sing a slow song and match my rising to the song) as well as taking long deep breaths. Once she slowed down, then I would give her a bit of rein, let her stretch her head down and then bring her back to a walk.
So she basically realised that she would get a reward (stopping work) if she slowed down to a nice trot. I also found that the slightly looser rein (for the moment anyway) and stretching her head down calmed her which was the main problem. Once she calmed down, she trotted calmly too. I then began to ask for a nice circle at a calm trot before she could stop work. Each time they speed up, do the same as above, but don't let her walk until she has given you a calm trot (I always used to do that but I realised I should rather ride it out till she calmed down else I was rewarding the bad behaviour). And now, my mare has calmed down, realised that a nice slow trot is much nicer for her and for me. I think once your mare calms down, you will relax too (the deep breaths and singing really help too!).
I havent progressed to slowing my horses canter just yet (we're still working on our trot and jumping but when I do, I'll share any techniques that work =)