As for the stopping, a simple voice command and sitting deep should stop her. Putting your feet forward is fine, but do not press on the stirrups. That's bracing, and as you've probably noticed, it doesn't work on your horse. :)
You shouldn't need to use a rein command, especially on a reiner horse.
Sit deep, STOP following the movement (freeze your seat), and say "Woah". If she doesn't immediately stop, bump the reins (which will bring her to an immediate, if ugly, stop), and make her back up swiftly. She doesn't get to do a few lazy backwards steps. She ought to be backing up quickly.
Then give her half a lap of break, and then set deep, stop your seat, and say Woah. If she stops, be sure not to be caught off guard and end up shifting your weight forward. That will confuse your horse and she'll think you didn't want her to stop. If she ignores you, bump her with the reins to a halt and swiftly take ten steps back. Repeat until she gets the idea.
As for lungeing, I'd do free lungeing. It's hard to correct a problem like that with a lunge line, since it just gets in the way. I'm assuming you understand basic body language? Always watch her eyes. If she's behaving, allow your gaze to drift over to her neck. Keep yourself parallel to her. If you turn away from her, she's going to turn to you. If you turn towards her hip, she's going to turn towards you. Watch her eyes, and keep your shoulders facing her, and then use to whip to drive her forward. If she tries to turn at you, use the whip to push her away. If she ignores it, smack her with it. It's a lunge whip; it isn't going to do any damage.
Make her trot or canter away from you if you have to. Just get her away.
If she's ignoring the lunge whip and still trying to come at you, bring a dressage whip with you as well, and use that on her if she gets too close.