I had to overcome that with my gelding as well. Part of it was me not being comfortable picking an untrained horses feet ;) and thinking that how would I handle it if he kicked. Honestly, as long as you are standing right and have a good grip on her she can't kick to bad at you. When he tried a couple times, my farrier told me to NEVER LET GO and push it inwards so they end up kicking their other leg. Then once they calm down, take a deep breath and continue on your business. It's also harder for them to kick when you pull it straight back when you're picking (im sure you already knew that). Now if they are trying to REALLY lash out give them a big whop on the butt or wherever you feel comfortable. I mean firm! Not abusive but enough to say hey im the boss. Just like you go after her when she bites, kicking is not a habit that is acceptable. So you go after her with a sharp tone in your voice and make that situation uncomfortable. But just be aware of your surroundings so no one gets hurt. And she has to be on a really quick release tie just in case too. My gelding looked at me like "oh gosh im so sorry!" lol With the babies, like I said, you are always going to fight for something, but over time you will see it pay off. Now we're sure that she has no back or hip pain right? Because that would also cause to kick out.
I tell ya, that's sign of a great minded horse when they get themselves stuck in a pickle and don't panic. That's why I think she would make a great little mare with a lot of training. Congrats on having a good training lesson with her!