Round pen work is possible bc at this age you won't want to have long sessions. I like the idea of establishing authority with her in the round pen, but rock hard footing is very concussive. Do you stall her? If so, you could train her to halt, back and "walk on" with her halter and lead, and demand that she obey every time you turn her out and bring her in to be stalled.
When I first got my horses (1985), I had 6 in an outside herd and NOBODY wanted to be caught. (They were all broken, however.) I thought that maybe I could get a few interested in being caught by shaking the grain can by the gate. The herd leader didn't buy it (that day), so others came up to the gate, I haltered them, then lead them to a tie up pole and fed them their grain in their own bucket. Anybody who didn't come to the gate didn't get any grain. Day TWO, the leader was the first up. After that I insisted that each horse had to put his head over the gate, wait to be haltered, then quietly lead to his own spot for graining DAILY. They came out in pecking order and they went back in in pecking order, too. When I put them back in they had to turn, put their head over the gate and wait quietly to be unhaltered, bc I was very concerned about being run over and kicked by horses that didn't know me well. You can do the same with her. I taught my 16'3hh KMHSA gelding to do this, and now he ALWAYS walks around the open gate, puts his head over the gate and waits to be unhaltered. My gates and fencing are a little tall
But my 5yo QH will put his head over if I insist, although he's not trouble to catch and doesn't pull away when I turn him out. I suggest you look into Clinton Anderson's videos. Two year old horses are very reactive and you'll want to be especially patient, and PRAISE, PRAISE, PRAISE for ANY effort, so that you show her that you are a benevolant leader. =D