You guys look great together. For her having been a lesson horse, she looks very responsive... I've seen some real disasters come out of school programs. One point of advice on her throwing her head in on the circle (and you've got the beginning of it by riding with more outside rein) is to shift your weight a little bit onto your outside seat bone. This gives her freedom to lift her ribcage and bend on the inside so she won't feel like she needs to fake the bend with her head. Ponies tend to be a little bit more sensitive to weight aids that larger horses. I saw this great clinic video on youtube before where this guy teaches a student on a lusitano how to get him bending better into half-pass by shifting her weight to the outside. By the end of it, he's doing half-pass and shoulder-in from a pretty much slack inside rein. Cool stuff!
OK fine... I found the vid for you, lol
I recommend watching all six parts. I know it's advanced stuff, but it has implications for other movements as well. Good luck and have fun :)