Rhiannon:
see this month's issue of Muscle & Fitness Hers for an article on training the body uni-laterally, one side at a time. It could help to lessen the definition and strength differential between the two sides of the upper body. It probably will never eliminate it completely , however, unless you can re-learn how to become ambidextrous!!!
I am right handed and can handle significantly more weight on that side, and it will also be so, but I am acquiring definition on both sides pretty equally. I don't know what else to tell you I am afraid. maybe others can address this issue?
Do you favour barbell training for the upper body over dumbell training? One problem can be that with the barbell the dominant side will naturally step in to take more of the load to help the weaker side out so you can keep lifting. Try substituting work like Crazy 8's for biceps which Cathe does with the barbell for dumbells only and see if this makes a difference. You can find substitutes for most exercises that will allow you to train one side at a time and/or use dumbells only.
Clare