I would suggest free lunging her, first. It'll get her to pay attention to you without having something pulling on her face and distracting her.
Before I go right into it, I just want to tell you this quick story about this gelding I had.
Beautiful horse, extremely smart. Very abused and totally an emotional wreck. I would get halfway up into the saddle and he would take off at a full out run and I'd have to fight get him to stop.
So after three days of this I decided, all right, you want to run, run then. I didn't ASK him to run, I just leaped on (literally, as he was already running lol) and stayed up for the ride until he decided he had enough. Once he stopped, I let him catch his breath for a moment, then started his lesson as I would if he hadn't run in the first place. Walk, jog, lope.
Sure enough, by the end of the week he was standing there like a charm for me to mount and dismount. Why? He figured out that running away did no good. I didn't have to fight with him, he never got hurt, and he realised that he was simply wasting his energy.
The reason I brought that up is because it sounds like your horse is doing something of the same sort.
If she's running as soon as she gets into the round pen, let her go. Wait for her to finish her little rant, then do your lesson. Don't use that as her lesson, though. When she has decided that she's had enough, ask her to walk around, then jog, then lope.
If she starts running as soon as ask her to move, then keep her going. I'm curious to know if you've ever joined up with her. That might be something to try.
Keep her going, and you'll notice signs that she's asking to stop. The flicking of an ear on you, licking her lips, lowering her head. Then stop asking her to move and she should stop, but only let her to do so when you ask.
Your body position is very important with this. When you're asking her to move, keep yours back straight, shoulders back, and head up. You're the herd boss and you need your body to reflect that to her because she can't read your head. Stay position with her shoulders so you are driving her forward, and not chasing her.
When you want to her to slow down or stop, step in front of her shoulders to block her movement. It may take a while but you will begin to notice that by simply moving in front of her shoulders a step or two with bring her down from a lope to a job without you ever having to say a word. When you want her to stop, step in front and say "Whoa." with a more relaxed body position.
I would suggest just completley losing the lunging whip and simply (yeah, simply! LOL But you know..) get her to move off your body.
I disagree that lunging is hard on a mature horse, or one still growing so long as the area being lunged in is big enough that they are running completely balanced (ie/ with their feet underneath them - you see some horses lunging in a pen and their feet are towards the outside while their body is leaning inside) and not overly done.
Being chased around in the pasture and jumped on by another animals weighing a 1000lbs is much harder on them than running around in a circle.
Lunging is also a good way to keep your horse focused on you as their leader, and allows you to check for any signs of lameness before riding.
Anyhow, hopefully I helped some, and if you have anymore questions I'll try and help!
Good luck with your mare! If that's her in your avatar, she sure is a cutie! :)