Do you know parents at either school? As much as I wanted dd to be with her friends, I also considered which parents I knew/liked as school friends/their parents will become a huge part of your/dd's social contacts.
I empathise with your dilemms. Dd is also in a nursery attached to an independant school and we are umming and ahhing about moving her and trying to apply for a reception place at an out of catchmetn Catholic school (we are practising Christians but not Catholic) on the basis that it is free and very good academically.
We have decided to stick with her current school as we have both fallen inlove with it and academic results are not everything imo.
Has your dh visited both schools, it helps that mine is a teacher and so fell in love with the independant school when he visited and he also wants her to progress to their senior school rather than our dump of a local high school.
Have only ever had the state vs independent school hypothetically, but know that DH occasionally daydreams about what we could do with the £6k we'd save.
TBH, I'd be inclined to keep her at the independent school. It sounds as if your DD definitely needs some TLC and personally I'd rather leave her where she's happy than risk a repeat of what she went through before. i think the "gut" thing about schools can be hard to explain to some dads. When we moved I (and DD) had an overwhelming gut reaction to the school she now attends. DH (ever practical) wanted her to go to another independent school which would have meant us moving closer to his workplace, as he honestly thought they both seemed very nice, better than her previous school, and for him living as close to the workplace as posible is everything! I'm afraid I just stuck to my guns and let him sulk for a few days.
Also, although good results in SATs are undeniably reassuring, sometimes the pressure to get good results can make the school a bit "hard-edged" IMO. My dsis (reception age) has just been pulled out of a primary school people scheme to get into because she needed a bit of "looking after" but the teachers were not prepared to give an inch.
If you had them in 2 places how would that work from a logistical point of view. We've had a similar dilemma and it would not have been workable to have had them separated, so both would go private or state.
Does the independent go all the way through, or would she move again in a few years time, and will there come a point where fees rise so you would need to review it from that point of view. Have you visited the primary to compare ?
Orinoco I would be seriously worried about a head which said they would teach my children by their age, not their ability, whichever way their ability was. How can this school get such a good OFSTED if it not matching the work to the children's ability?
IMHO, your child's happiness is more important at this age than academic achievement. As long as it's a decent school and she's reasonably bright then she won't have a problem with learning. I think personally that socialising is much more important at that age than how many boxes you can tick.