Young kids are going to take forever to learn kata or "forms".
I am a black belt and have learned traditional Shotokan kata (Heian series, Kanku Dai, Tekki series, etc) as well as Kempo forms (star block/short forms, long forms and a few others)
It is typical that your child takes a considrable amount of time to learn a form given her age. If you want to have a video showing the moves, have the instructor perform the form for you while you video record it. Ask him to do it full speed, then explain it step by step, and then full speed again all in one recording. This will help your child remember.
I prefer a japanese traditional Shotokan style, but my school's master actually studied under Ed Parker, who started the Kempo style. I have made my own style based upon what I prefer but take techniques and approaches from both styles of Karate. I still train both styles.