I can't imagine how someone who attempts (key word) to teach three year olds gymnastics on a daily basis could think that a three year old, any kind of three year old, doing a pullover, getting her head up, then doing a cast back hip circle and a stalder press with fairly straight arms is anything short of extraordinary. That is basically the definition of extraordinary. To put this in perspective, most 3 year olds cannot skip and only about 50% can do an unspotted front support forward roll while a good portion can't even attempt it with an iron grip spot.
That said if she really goes 20 hours a week that definitely explains some things to me and makes my head spin. I still don't think "any child could do it" because most children simply couldn't even attend and participate in that amount of practices. It really wouldn't matter.
I would never choose or endorse this path, but she truly is built for gymnastics as such likely will not be as affected by doing this stuff as someone who isn't built for gymnastics. But still, why take the chance and all, I'm 100% on that side but I am compelled to point that out. Because even doing everything "right" someone who is genetically less suited for gymnastics is going to be more prone to injury than someone who is more suited physiologically and messing around. Mostly because I think that reality is sometimes underappreciated. But still yes, for the love of gymnastics, no preschool head springs.