Mine went to independent secondary school, as they were at a nice small primary and I haven't ever seen the point of primary stage independent fees. If anything the kids we know who went to pre-prep, prep then senior etc just came out in a bit of a bubble and didn't have any friends outside of independent school circle.
The value added in my experience increases as they get older. By 6th form, it's a big impact to go to independent over state.
It's nothing to do with grades or academic ability IMO. Not all independent schools are selective, and as others have said you can get great teachers and top grades in state schools. It's about everything else - the enrichment, talks, trips, events, who they meet and who they're friends with, how they speak. It's social capital which then gives them advantages in life. (It's totally unfair of course).
Kids aren't made fun of for being clever, not wanting to vape, enrolling on D of E etc. They can safely be boring, no make up, no drinking etc if they want to. If they have a particular talent, they can pursue that to a much higher standard and have the opportunity to share/compete with experts inside and outside the school because of the connections they have.
That's why we paid for it and why we think it was worth it.
In your situation I'd choose a state primary carefully, look after how your DD goes through school and how she talks, sign her up for hobbies etc, and start saving now for DD and DC2 fees for senior school.
I absolutely would not consider sending one child and not another, because of all the advantages above. I've seen it with cousins, their paths just diverge and it's stark.