Re: Lunging issues
My advice to you both would be to start from scratch with the mare, without assuming that she knows anything about lunging.
In-hand work, such as teaching her to yield to pressure on various parts of her body, is probably the most important part of teaching lunging. Teaching her to yield her neck and shoulder away when you step in toward her will help when you send her out onto a circle, and will help you dissuade her from falling in or turning to face you.
Running off on the lunge rein can be a favourite evasion of some horses. It could be that she has been badly lunged in the past and has genuinely been made afraid through the experience, or she has maybe just run on and been stopped and this has taught her that behaving like this gets her off work.
Sending a horse on a circle involves driving the back end forward. If too much pressure is put on, the horse may turn to face the handler. The over-use of a lunge whip may have this effect. The art is to encourage forward movement without causing or allowing the horse to turn in, and this is why its important to teach the horse to yield its fore.
Horses which run on on the lunge are a bit scary, but to begin with it is best if they can be kept going, rather than stopped or attempts made to slow them, as this causes uncertainty in the novice horse and they will be more inclined to evade. Once they are going forward without falling in or evading by turning, they can be kept going until they settle, and then asked/allowed to slow down.
See my reply here http://www.equine-world.co.uk/horse-forums/showthread.php?t=33975&page=3
for further information.