Clearly this teacher has failed, or will fail, her NQT year. If she cannot teach 13 children, there is no career for her in the future. I am amazed she got through teacher training! I am also amazed a school can afford 13 children in a single class and a TA. It must be very well off primary school! In addition, the school should have taken action to remedy the poor teaching much earlier. It is not acceptble.
I do not think the OP is pushy at all. Lots of parents have reasonable expectations of teachers and the OP is being very reasonable. My DD could do a lot more than this at age 4 - as she was in YR.
I think, OP, I would start talking to Y1 parents and see if they are happy. Have their children flourished at this school or not? Is your DD going to want to work in Y1 if she has had an easy time in YR? That might concern me.
I am also amazed that this teacher was not closely supervised. All NQT staff must be supervised, monitored and advised and the Head should have got a grip with this situation. It is not up to a TA to whistleblow! Neither is it up to a teaacher to "invent" the curriculum. I therefore, would have great concerns about the Head and the fact that that they have not put interim measures in place to accelerate the learning of the children in YR when they knew there were problems. What has the Head done to help these children and overcome poor teaching and progress?
Therefore, do not be reluctant when asking about plans for Y1. Ask to see the curriculum and, especially, how they intend to get children, who have not been properly taught, up to speed. This is vital or your DD may not access the curriulum in Y1 very easily.
I think I would now want concrete information and evidence about the school on the progress DD has made to date and what she needs to work on to help prepare for next year. Do they have advice for parents with writing and maths for example? Practice over the summer?