Does your son ride without training wheels ? (I assume, yes) Is there anything wrong with allowing her to use the training wheels until she sets the challenge for herself to be like her big brother and give them up ? It would be a whole lot less fight. (And for the past TWO summers? Did you really start pushing her to ride on two wheels at age 4 ??? What ever happened to allowing your child to BE a child for a while and to grow up at her own pace, not become a teenager overnight?)
If you MUST push her into panic so she learns to accomplish something she doesn't want to do, the best method is to leave one as it is, and shorten the other about an inch. When she tips to the shorter side, the training wheel will stop her, but there will be a bit of time in there where she will learn to lean back to the middle. She'll basically be riding on 3 wheels instead of 4. You can then raise the other training wheel about an inch. It will be there to catch her, but when she rides upright, she'll already be on only two wheels.
The best way I've seen kids learn, however, is to have them on really small bikes while learning -- bikes that are actually too short for them. From there, they can pop legs out to keep themselves from falling, they are closer to the ground, and they feel safer. It's kind of like the difference (for you) between sitting on a Shetland pony or sitting on a Clydesdale. On the former, you could drag your feet, or stand up and the pony could walk out from under you. On the latter, you are WAY UP HIGH and are in many ways at the mercy of the massive beast below you. (yeah, I know, the beast would probably be a trained one, but even then, you only have as much control over a horse as the horse is trained and willing to give you. It is the stronger animal). So, if you have a small bike she rode when she was littler, let her try on that one. Or, play with the training wheels a bit . . . but remember that her fear is real, just like sitting on an elephant. Your goal is not to scare the bejeebers out of her, but to help her accomplish something. So don't push. Help her to build her confidence, help HER to win. It's not your game, it's hers.
(Also to consider: do you let your kids ride on the lawn? Ours don't, but the lawn is a much more forgiving surface to fall on than the driveway)