You need to get her hip under her and make that front end light. You can do this on and off the pattern, and this is something I have to do often on my mare.
The easy one is just keeping pushing that hip in. When you do your rate exercise, stop at your rate point, push his hip back under him, carry on around the barrel with a lot of bend and then when you leave it and his hip clears the barrel go ahead and push it in again. That one's easy.
The second thing I would do is something similar to what Sherry Cervi is doing here: https://www.youtube.com/watch?v=G14k0S4Eato
She is doing turns on the backside of the barrels with a lot of bend. I do a lot of these. My mare is naturally on her front and requires a lot of drive out of the barrel and this is a great exercise. It says, "You better get your hind end down because your front end has to do something now."
It also works on stops for reining horses. Everytime you stop off the pattern, before her feet even stop moving be kicking her into a haunch turn or a spin. Doesn't have to be perfect so long as her front end moves. Be aggressive. Then walk off and relax, pet her, etc. That exercise will get a horse sore, I can only do it four or five times on Selena, but if your mare is in shape it shouldn't be a problem just so long as you can read when she is starting to listen.
Also rollbacks into the fence. Give your rate command, turn her into the fence and make her DRIVE out of it. Even if the turn isn't good at first, kick and get her out of that with a 110% energy. Then bring her back down to a nice, relaxed gait, and let her clam down before doing it again. It gets that energy there and the horse will learn to get the front end out of the way because they can't drive off with that energy if their back end isn't in the ground.
Hopefully that will work for you.