It takes me around 2 years to completely train a barrel horse. Generally the first 4 months are just walking and trotting the pattern. After that I slowly will add a lope between the barrels, but I drop down into a trot around the barrels. It's easier to control them when your going at a slower speed. This will allow you to enter and exit the pocket accurately. I also tend to push my horses past the barrels by quit a bit because when you do start adding speed, they tend to get it in their mind and cut the barrel too soon. So I add an extra 5-6 feet in my pocket for about 8 months, then I slowly over the next couple of months I'll get them closer and closer to the barrel.
I don't start pushing them into the turn at a lope until I know for sure they they know what they are doing. A lot of times, I'll ride on a really loose rein and see what they do when the pattern is set up and I point them in the general direction of the first barrel. 9 times out of 10, they head straight for the pocket just the way I taught them.
After about a year, they are high loping a nice, consistent pattern, and I let them do that. I don't push for anymore speed. A lot of times a horse has to learn how to run anyways and eventually they naturally start adding speed themselves. The only thing I'm concerned with after a year, it a super nice, clean, smooth, safe pattern.
Once I'm comfortable with the high lope, I start pushing for speed. But this is usually half way through their 2nd year of training. So they've had 1-1/2 years of walking, trotting, and loping the pattern. I don't use spurs, and I don't use a crop on these horses. I do use a crop on my seasoned horses, but they have years of racing under their belt.
And I never start a horse on the pattern until they know all of the basics. Walk, trot, canter, whoa, back, side-pass, leads, flying lead changes, roll-backs etc.
Retraining a badly trained barrel horse is the worst! So take it slow. It's the best thing not only for your horse's body, but his mind too! Your mare is already showing classic signs of a hot-headed barrel horse. The prancing, tossing of the head, hopping around, etc. I do NOT accept this behavior from my horses. I want my horse to have a sane mind forever. I want them to listen to me when I'm on them and a lot of barrel horses are so focused on RUN RUN RUN that they totally forget about their rider and become dangerous under saddle, not only to their rider, but also to the riders and spectators around them.
"The greatest pleasure of a dog is that you may make a fool of yourself with
him and not only will he not scold you, but he will make a fool of himself too."