Don't let her get fast. Keep half halting every so often and do some figure eights or circles every now and then.
Since she is green, she may not understand what you are asking when you half halt. She MAY toss her head and brace (because tossing is a sign of discomfort and thus cannot be relaxed) because she's anticipating your strong reaction.
Walk me through the steps you do to ask her to trot, etc.
She should not be attempting to "collect" if she is still green. Work on a loose rein, w/t/c, and when she's got that down, introduce lateral movements, etc. and THEN you can consider working on using her hind and collecting up.
Collecting is VERY hard work, even a horse engaging their topline is hard work.
Don't expect so much from your horse. A tossing head tells me: "I'm not ready for this" "Slow down" "I don't know what you're telling me to do" "I don't like this" "We aren't communicating."
Just some thoughts.
"Strength is the ability to use a muscle without tension"