The majority of your post is regarding your DD's academic level & whilst I understand the concern around the grammar school intake, a child's time at school is not solely for achieving academic success. Does your DD2 have friends, is she playing with her peers, does she enjoy school, all of these are as valid as the academic side of things.
In my experience then state schools want every child to succeed with the parameters set by the powers that be, if Ofsted say that 2 levels a year should be aimed at then once a child achieves that level then there is not much more pushing beyond that point. I have a G&T child & we changed (state) school as he was not being challenged at all, to another state school where he is being challenged. If your child is not in the top 2 sets already, then (& I really don't mean to be offensive) but perhaps she is simply not clever enough & all the pushing by the school won't do that much. If you think she is in the wrong set & could handle the more difficult work then speak to the teacher, they will know what level your DD works best at. The new school could promise the earth but until your DD is in their classroom they will not have an idea of her ableness so any promises made now would be meaningless, no school would push a child beyond 2 levels if the child was unhappy working under such pressure. Taking that forwards, even if DD2 did get into grammar would she be able to sustain working at that level happily? Would she thrive socially & academically in that environment or would she be happier in another less pressurised school?
Also keep in mind that school is not responsible for 100% of a child's education, so maybe start thinking around music lessons or sports outside of school. If your grammar has an interview process then a well rounded or accomplished child would stand a good chance.
Its a difficult one, I moved schools & I don't regret it for a moment, but simply moving school because your child is not achieving what you think she should be achieving, regardless of how well your DD is settled makes me uneasy. It could be that the new school will push her a lot further, but if she is unhappy in the new school that her work might go to pot regardless.
Step back from the academics of it & take into account the whole picture, academics is not everything :)