I'm no expert but it sounds as if someone has overdone the join-up with this mare. She has learnt that if you go out to the edge of the round pen you have to work, whereas if you stay close to your human in the centre you can rest. You're right that it does sound like she does it to evade work.
If you have someone to help you, try lunging her on a line with one person in the centre and the other leading her round the circle, until she gets the idea. When you stop, always go to her to pet and reward her, and let her relax out on the edge of the circle instead of asking her to come in for her rest time.
When you walk away from her, if she tries to follow you need to get very firm. Use the lunge whip on her shoulder to keep her off you. If you can at least get her walking forwards reliably, you can then adjust your position until she's doing a circle around you, and then keep pushing her outwards to increase the circle size. So first of all you need to establish independent movement on her part.
There is nothing more peaceful than watching a horse eat.