We can't decide!!

same as above really, private sounds a good option for your quiet but enthusiastic dd but only if you can do it for your other child...and dont get unexpectedly pregnant with a third child like I did- 3x school fees = nervous breakdown ;-)

Private if you can really afford to do for for both.

State if not - you have no real reason to send the oldest privately from what you've said. It is possibly dd2 when her turn comes may " need" private education more eg need to be in a smaller school for fear of getting lost in a big school etc etc

The indie is selective so don't be fooled by their excellent gcse results - if ou only take kids working at level 5 in key stage 2 SATS and they don't get results like that you are failing them- the comp takes everyone- including learning difficulties/ no parental support etc.

Can you afford to send DD2 to the same indie? If you can't will this bother you? We have DCs at both. They were educated privately till 13 then one stayed in indie ed. and the other is at our excellent local comp. I knew nothing about state ed. and am surprised and pleased at how good it can be. I'm in my 40's my state ed was not that good then so font necessarily let your experience sway your decision.
Your head thinks your daughter will do well anywhere so it's down to personal choice; can you really afford it? Have you taken the extras into consideration? Will you have you sacrifice other things? If yes do you all want too? Be honest with your self some people like to send their DC's to private school because they think it looks good one friend hideous mother women I used to know liked the fussy uniform at her DC's prep "when Im in sainburys after school with my DC's it tells other people I have enough money to pay for education!"
Having paid for education for the last 12 yrs IME when it's really good it's marvellous and worth all the sacrifices we have to make when it's anything but really good it's can be frankly mediocre and unless your circumstances are complicated or you're absolutely loaded probably not worth it if you have a viable free option.

I agree with you DH- if you can afford it, go private. The GCSE data you quoted says it all -better results are had at the private school you looked into. Further, your very own experience tells you that your comprehensive probably wasn't the best choice for you, so why should it be for you DD? If you're considering how many of her friends will attend her school, that is irrelevant - she will make more friends where ever she attends. If you are considering the proximity, ie, 10 minutes vs 20, - that really shouldn't be a consideration, should it? Well...ultimately the decision is for your family to make, but in my opinion, the choice is clear. Best of luck to your DD whichever you choose!