Flip the line means jerk it HARD a few times.
After she has learned to walk on the lead, if she is still crowding you and stepping on you, here is a tip I would use this as a last resort as I have only tested it once:
So I had a 17hh overo mare that was constantly intruding and bumping into me and stepping on me. I go so sick of it one day. I took her into an arena, then I walked around and then come to a fast STOP (not a stop one more step, a STOP) and if the horse bumps you hard or steps on you, turn around fast and give her a kick on the leg, Not like abusive, but enough to get her attention and make her think "ouch I don't like that." Horses tend to respond to pain, but pain should be used as a last resort. If you were sitting on a horse and it began bucking, you should whip it but again not abusive, the horse will definitely respond to that. Do that walk stop kick thing a few times and TRUST me the horse will be trying it hardest to stay away from your bubble, and it will have its full attention on you. Now the horse may also rear and fight a bit after the kick, so wear gloves when you do this.