Some people I know have got themselves into a massive mess while trying to finance private school without the means for it.
They sent their DD1 to private school while in a fairly precarious financial situation, and hoped for the best. Predictably, things went wrong as they weren't prepared to compromise elsewhere in their lives (and chose a stupidly expensive school for the 'experience' it offered) and they struggled to pay the fees. Despite being in arrears, they somehow persuaded the school to let their DS start, and then to give them a grace period on the basis that the financial problem was short-term. The school finished up kicking the kids out mid-term when it became clear that no money was going to be forthcoming.
They moved the kids to another private school, and still can't meet all their financial obligations. But they're obsessed with the idea that no other school can possibly be good enough. Despite living in an area stuffed with good and outstanding schools, which they'd be able to get a place at with a very short wait. They're in real danger of going under, but they will not give up the private schooling idea.
The bottom line is that private education is expensive. You can either afford it or you can't. If you can't, you can't. We are hoping to be able to afford private secondary, but we can't manage private primary. We also have a back-up plan if we get to secondary age and can't be sure of affording it, and we won't even try if we can't be sure of sustaining it right through to the end of school.
I think the worst thing you can do is to start a child at a lovely school with tiny classes and all sorts of extras, and then finish up having to pull them out. On that basis, I'd be inclined to let your DD stay, but make no attempt to get the other two into private schools as it's clearly not sustainable.