How do I start training her more.... we have accomplished the pattern, but running it (trot, lope) she minor spooks. Like running WAY around the barrel & doing a little buck or kick around the barrel. Any advice???????
It sounds like you just need more work on the pattern and more work on controlling your horse.
Make sure you can control your horse's body any way you want at any gait.
She should move away from your leg pressure. So she should be able to sidepass from a stop, or move diagonally at any gait.
She should stop easily from any gait.
She should be able to pick up on the correct lead that you cue her for.
She should easily back up when you ask.
She should be light on the bit and respond well to neck reining and direct reining at any gait.
You should be able to have control at any gait - especially the gallop.
The fact that she is running wide around the barrels suggests that she is not ready to be going faster (needs more slow work on the pattern) and that she needs some more training from you.
How long have you been training her for the barrels?
Keep in mind that it takes anywhere from 6 months to 2 years to completely train a barrel horse. One of the things that will ruin your horse's progress is by asking her to go faster than she is ready to go.
So if you can do the pattern perfectly at the walk, great! Keep doing that, because it sounds like she cannot handle trotting yet at this point.
Remember that you don't have to do the pattern over and over to train a horse for barrel racing. You can do lots of the same maneuvars required in open space.
You can practice trotting and loping circles. Really try to make them perfectly round and control her speed exactly how you want it. Do some faster, do some slower, but always make sure you are the one in control of how fast you are going.
You can practice rollbacks. Start by using a fence to help you (turn into the fence) and eventually work to do rollbacks in open space. You can do them at all speeds (walk, trot, canter).
You can practice two-tracking where you ask your horse to move diagnoally away from leg pressure. So if you want to two-track to the left while you are walking, you want to tip her nose very slightly to the right, keep your left leg OFF your horse, and apply pressure with your right leg in the middle of her belly. You can make two-tracking more difficult (once you get good at it) by either doing it at faster speeds, or by asking her to tip her nose in the direction you want to go (counter arc).
And if you are unsure on how to do anything of these or how to train any of these things, all you have to do is ask! I can explain.
Also, are you warming her up adequately before you trot or lope the pattern? (Although you should not be galloping the pattern if she cannot handle trotting it ... that's going too fast before she is ready and will create bad habits.) Maybe she needs more time to warm up and get rid of some of that excess energy of bucking and kicking.
Or, it could be that she is in pain somewhere. Make sure your saddle fits, make sure your bridle and bit fits, make sure she has no dental problems, make sure she has no feet problems, and make sure her back is not hurting. You are best to consult with your equine vet, chiropractor, farrier, and dentist for these things.