That is all fine and dandy and its great she made that little horse work for her.
But my point is, that doesn't always work. I'd tel you right now that MOST of the people who try this ruin their horses. I have seen wonderful, bombproof kids horses get turned into running, spinning, rearing, bawking psychos because someone took them and tried to train themselves.
To the OP, PLEASE seek a professionals eye. It is best for you and the horse. I know it is hard to accept that sometimes you can't do everything yourself because I've been in your shoes before, and once I started working with a trainer I realized how much I didn't know and how with just a weekly lesson how much better my horses got.
Do this now, you will learn enough to take a horse with a foundation and turn hi into a great barrel horse. You need to teach all the buttons, the rate, the smooth motion turn, the powering out, hip control, correct body position, counter flexion, expanded turns, quarter turns at the canter, rollbacks, just to name a FEW.
I'm not trying to discourage you, I just want you and your horse to do yourselves justice and know that not everything can be done on your own. There is no shame in getting help which will help you in the long run.