This may sound a bit backwards, but have you tried lunging her without the whip?
I tried several times to get my horse to free lunge with a whip, and he simply would not. He would stand there and look at me like I was insane, or dumb, (probably both) and toss his head up and down.
The other day I just used a coiled lead rope instead of a whip and sort of swung that (still coiled) around to get my point across, and he went perfectly. I never had to touch him with it. All I had to do was, for example if I wanted him going to the left, I would point my left hand in that direction (about parallel with my shoulder) and raise the leadrope hand and off he'd go.
I walk a small circle in the middle (same direction as the horse) once he's going just so I can drive him better; just be sure to stay slightly behind the horse, so you're driving him forward from his hindquarters.
Also, never look at their face; I like to look at Beau's hindquarters when lunging but I also know of a trainer who looks at the shoulder when driving forward.
You need something that makes a strange noise. When I teach horses to freelunge I use a chain lead and make the chain end jingle and use the nylon end to toss towards the horse. It usually works. If that doesn't work attach a plastic shopping bag to the end of the lunge whip and wave it around. If that still doesn't work then you need to do some moving yourself, chase her with the bag and lunge whip or chain lead. Don't hit her with anything, that will just make her afraid of it, not respectful of it.
May I suggest that your horse is simply confused and if you were to break things down into simpler steps, you may find that she will respond more readily. What I do is separate everything into simple movements- forward, stop, back and turn. I train the horse to respond to those simple movements and then start to combine them. A circle consists of forward and turn, both of which will have to learned separately first before combing them. So you might want to train the horse to walk and trot a square first using a 12' lead rope. As the horse begins to understand, he will begin to combine the simple movements into a circle.
As to the rushing in at you- horses do what they are rewarded to do. While not intentional, somewhere along the way the horse has received enough rewards, at doing this, that it is now a habit. The fix is to simply not reward him any longer. This may come in the form of a sharp enough rap with your training stick that the horse understands you mean business.