Neither video was slow work. Both were cantering/running.. She needs to be worked at a walk and trot for a while. Honestly, I would trot to the barrel, say "Whoah." firmly at the barrel and make her walk around it. She wants to go faster? Just keep making her go around the barrel until she is listening. Have you considered that this mare may need other outside work? Like trails etc. Get her away from the barrels sometimes? Not saying you don't. She looks out of control at the show. And I would have been so far up her butt for that, she wouldn't know what to do with herself. That is not acceptable at all. She DEARLY needs to learn to walk and trot the pattern only after she is walking it without any issues. It would be in your best interest not to allow her to run the pattern anywhere until she is walking is perfectly, then trotting it perfectly, then cantering between barrels slowly and calmly and trotting around them correctly, with no fuss. Until then, I don't believe she should be allowed to run them at all. This is out of control, and very dangerous. As the other member said you may be able to fix it and you may not. If she won't stop this, and you can't fix it. Then her barrel career needs put to an end.
Never let "good enough," be good enough.