First of all, have your vet or equine dentist check your mare's mouth for sharp teeth or the presence of wolf teeth. Check the bit for proper fitting. If the bit is properly adjusted and her teeth are in good shape, you might try schooling her in a drop noseband. I do not recommend going to a correction bit until your filly yields to your leg and stops promptly when you ask. A correction bit is a leverage action bit with jointed mouthpiece and a port. While it can be a good bit to soften an older horse, going to such a bit before your mare has the basics established will only cause you more problems in the long run.
Time spent in performing leg yields, circles, and squares, half-passes, half-halts and stopping on command will result in a mount that is prepared to go on with her training. At 4 yrs, she is ready to spend the time working; you can push her without fear of harming her, assuming that she has no physical problems to limit her.
This article is published here with permission from Western trainer, Sandy Arledge and Horse Illustrated July 2003 issue.