Eesh, I know how frustrating it can be riding when it seems all the horse wants to do is get rid of you. I feel for you.

Maybe Ava is too tense in her back and she bucks to relieve the tension. It's most likely nothing to do with the way you ride her, some horses just tend to stiffen up rather than stay active and supple. Try lots of transitions with her to begin with, like 2 strides walk, two strides trot, over and over until it's perfect. Ava really has to listen to you to get it right and by concentrating on you she will lower her quarters, become more accepting of the bit and a little more supple in the back. If Ava is capable of extending and collecting paces this could help her too. One thing I have read that I've found helps me a lot on difficult horses is aim to do 100 turns and 100 transitions in half an hour, it sounds like a lot but actually you can do it pretty quickly. Maybe Cherokee could benefit from this type of schooling too as I read about his behaviour in your other thread.

Have you tried lunging either of them? By putting the tack on them and then letting them work off some steam for 5 mintues before you mount will help to get them on the bit and working in a good outline. It may sound like that won't help with the rearing, bucking etc, but if you concentrate on maintaining the feel of the horse in a good position underneath you, the horse has to concentrate on that rather than what may frighten him/her.

I hope everything works out for you and the horses!