For the off balanced mare, dressage training would be a great place to start. Getting her to use her body properly will help develop the muscles she needs for good balance. Lots of trotting, circles and suppling exercises.
For the bucker, I'd have someone take a look at his back and hips to see if it's a pain issue. If it's behavioral, he's probably just one of those horses who needs to be ridden more frequently. Horses that act out usually are smart, easily bored and need a confident leader/rider.
Like others have said, TB's can do any of the english disciplines. I'd start with dressage for both of them, get their muscles built up properly, and then you can move onto jumping.