We don't bite so hard.
Everyone has got to start somewhere! And I am no expert by any means; everyone can always learn something from someone else.
First of all, your mare is gorgeous! I love her!
It is good that you are not letting her go full-run speed yet; she is certainly not ready for that. However, I would encourage you to even slow it down a step further at this point. She doesn't appear to be ready to gallop the patterns yet. I want you to succeed and trust me: If you create bad habits now, and practice those bad habits over and over (so they become engrained in the horse), they are very hard
to get rid of. I can say that from experience. The best part about learning, is you can learn from others
mistakes, so you can avoid those same mistakes yourself!!
Don't think of this so much as a critique or critism, but as ways to grow, learn, and improve!
First thing I notice at the beginning of your video, is that he head is rather high while you are holding her up, which is making her back hollow out, which is making a rather rough ride! What bit are you using on her? It would be beneficial to work on some breaking at the poll exercises and some collection exercises. You want her rounded and collected when you approach the barrel, in order to make a smooth turn.
I also would shorten your reins up a bit. If you want your hand in the barrel turns, it is quite far out to the side. You don't really want your hand to leave the "imaginary box" around your saddle horn. You want to keep your hand quiet and low, and simply guide her around the turn. Going back down to the trot will help with that because you won't have to worry so much about constantly try to slow her down. And if these are small local shows, no one is really going to care if you trot her through the pattern. I much prefer to see a horse and rider doing the patterns slow and perfectly correct, than see someone blasting through the pattern in sloppy fashion because they are clearly not ready to go fast.
Going around the second barrel, her nose turns with your reins (again, too long) but her body does not follow. Practice doing one-handed perfect circles away from the pattern so she keep a perfect arc in her body, keeps her back rounded, and can make a perfect circle (at all gaits).
WAtching on the 3rd barrel (and really all the barrels), I want to be able to see a distinct cue to the horse to rate for the pocket. Usually, that's the rider dropping their weight into their seat, from the standing position they were just in for running between the barrels. That rate cue is your cue to your horse to set up and turn. So work on (at slower paces) making an obvious "sit down" cue for your horse to turn.
In the small 3rd barrel clip, you came into the pocket too close, which caused you to come out the backside too wide (to avoid hitting it). Again, at slower speeds, practice setting your horse up in the perfect pocket distance to complete the turn fully. When she's got it down perfect at slower speeds, then you can try to speed it back up to the gallop.
Keyhole ... that's okay she got a little scared! That's what seasoning is all about. I'll be going through that (again) next year with my 6-yr-old I am training, after I had to put down my good 1D/2D barrel horse this year.
When you go to make the turn in keyhole, do you see how you only used the reins? And see how only her head turned around, but not her body? This is where, again, a good rate cue can signal your horse to turn. When I do the keyhole, I keep my body position forward until the exact moment I want my horse to plant it and turn. To cue for that, I sit deep in my seat, use a verbal "hup!", cue with my outside leg, and finally (lastly) cue with the reins. Now, of course, these things all happen within a split second of each other, but they do happen in order like that.
So really work on legs, seat, and body with her and getting her used to those types of cues. You should be able to move her hindquarters, her shoulders, and her rib cage, all independently of each other, using your body and legs.
She looks like she's got a little gas pedal there .....
Poles. The first turn actually wasn't too bad! She did still get a bit front-endy, in that she swung her butt around in the turn. Really work with her on planting that butt (and you using that rate cue!) in a turn. YOu can work on this with rollbacks on a fence.
Also, I would definately slow your poles back down to a walk/trot and work on two-tracking. This just means that you are going to move her laterally between the poles with your legs only. Use your reins only to tip her nose very slightly one way or the other. You don't want to rein a horse through a pole patter, because that causes their head to be in the wrong direction (of the arc their body should be on) which causes them to shoulder into the poles. So if you want to weave to the left, you'll keep your left leg off the horse and "push" them over with pressure from your right leg. I can explain that in further detail if you need.
That way too, you are setting your horse up for the proper leg cues to do the flying lead changes in-between the poles.
And then it looks like we move onto Dixie! A lot of the same problems still apply. First barrel was okay (although the pocket into it was exaggerated). Second barrel she did not say on her butt through the turn, and you left the second barrel wide. You always want to finish each barrel turn, and make a perfectly straight line to the next barrel. The shortest distance between 2 points is a straight line!!! 3rd barrel looks like she turned too soon, causing her to come off the barrel wide to avoid hitting it.
Now is it worth to re-train Dixie at age 25? Maybe ... maybe not. That's up to you.
Overall, you are not doing bad at all! So don't take anything I said as "cutting you down". I used to be in your place too at one point in time!! (As all of us were!) These are just a lot of the things I have learned over the years, especially learning from the mistakes I made.
Precious looks like she has great potential. Now we just need to work on a few training elements and a few re-patterning works at a slower pace, to get her to the top.
I hope for a speedy recovery for Precious! I went through the same thing with my old barrel horse, Beau. When he was 5 years old, and just starting to "click" on the patterns, he dang near cut his own foot off on the barbed wire fence. I didn't ride him for almost a year. Healed up and by some miracle, came back sound. Until I had to put him down at an early age this year.
So I feel your pain!! Hope she heals for you.