My horse has cantering issues?

I have a POA mare with some cantering problems. When we bought her, we could not get her to canter. At all. Well, we got her over that, now she will canter and keep cantering until I ask her to trot. But she has two very big problems: she is unsteerable, and she goes at kentucky derby speed. For steering, she does not brace against the bit (she is in a smooth snaffle), I can turn her head, but she follows her shoulder, no matter where her nose is pointing. I can steer her with one finger at the walk and trot. For speed, she either ignores half halts or drops down to a fast trot with them. She has a beautiful slow trot, but a canter worthy of Secreteriat. Help?