What did you do during your meeting with the new student?
I don't understand why you're so conflicted on playing for the parents --- they are the ones employing you to teach their kids. If you sent your child to take pottery lessons with an artist, wouldn't you enjoy seeing the artist's creations?
Is it appropriate for me to play a solo piece at my student's recital as I am being asked by a parent to do?
As far as playing at student recitals is concerned, I personally would never feel comfortable playing a solo. So I'm with you on this. Certain negative and critical parents may even call you an egotist.But if the parents really bug you----play a duet with one of your students. Parents ALWAYS are so extremely charmed by this. They think it is just so touching how the excellent mighty teacher will play along with a little youngster. You'll be a hero. I learned this when I shared a recital with another piano teacher, and she played a duet with a five year old, and all the parents came up to me afterwards and said, "that was so cute when they played that duet. Oh I just loved that! Do you ever do that?" Of course I was thinking, "well, I do now."
You'll be a hero.