Yes, collecting would help that. Have you ever actually seen this mare run barrels? The reason I ask is because collection is a big part of barrel racing, it's required to get around the barrels. Instead of sawing on her mouth, but steady light pressure on both sides, and hold it until she drops her head, even the tiniest bit, then release. Keep doing it, and she'll get where when there is pressure on the reins, she will drop her head instead of raising it. At first she is going to try raising her head to avoid the pressure, just let her figure it out, hold the pressure until she drops it. I promise that she will figure it out. Before you can drive her onto the bit, you have to teach her to keep her head down, otherwise she will just raise her head and hollow her back out. Once she learns to carry her head correctly, you can work on her collection. I have an exercise where I work several small circles, into a four leaf clover kind of pattern, then lope a circle around the pattern. I'll get on my other computer later, and post the diagram, so you can see it. You start at a walk and work your way up, but take your time, it requires a lot of balance on the horse's part to lope the tiny circles in the middle. I'll try to get on there shortly and post it here so you'll have it.