Well, for some horses it's hard to be asked to be a gymkana horse (quick to start and stop, and go, go , go!) one day, and the next jog and lope ala WP.
So that's something to think about. She is not a machine that just does exactly what you want when you want without any memory from the time before . I mean she's a living thing and might not be able to do it ALL.
Ok, you said when you pick up the rein, she throws her head up. She must have some anxiety about the rein contact, and that would tie in with you saying that she does not collect.
Have you ever asked her to trot off or canter off WITHOUT picking up the rein? Try this first and let her go forward without any rein contact. Then try to slow her at first with only your body by becomeing heavier and kind of making your body like concrete and exhaling. Pick up the reins, but do it slowyl and you think , I mean really THINK, "slow , slow, slow" and breath out . You will lower the energy in your body, physically and mentally, she should cue into that and slow. When she does, cease your rein contact, even if she doesn't stop only slows. I venture to guess that whe she speeds up, it causes you to get tense (it does to most anyone, including me) and you then ADD energy to the two of you, so you must take energfy out by doing all this slowing and calming of your own body.
I might write more tomorrow, 'cause I am not sure how clear this is, it being really later here now.