I don't think it is confusing, because OP has clearly explained that the school wasn't their choice.
This is my understanding.
OP's husband had to pay ÂŁXX in maintenance (let's pretend it's ÂŁ2k).
ExW / Mum of kids - chose to spend that ÂŁ2k maintenance on private school. That's fine, she can spend it on whatever she likes.
But what's crucial here is that Husband and ExW did NOT decide together to send child to this private school separately from maintenance, that's just what she decided was the best use of the maintenance she received as resident parent.
Something has now happened that means the child no longer lives with mum, but instead live with dad and OP.
Technically what should happen is that her husband should stop paying maintenance and instead ExW should pay him.
However, if he stops paying maintenance then ExW can't afford school fees and child gets pulled from school. ExW apparently on low income so minimal maintenance anyway, but even if she did pay it, that would mean school fees couldn't be paid and child would be removed from school.
So ExH is still paying his maintenance (which ExW is choosing to spend on school fees), and he's not receiving anything.
ExW decided to use her maintenance for private school (as is her choice), but now OP and her husband are on the hook for that choice, despite the school being a minimum 45min journey each way. They're also paying all upkeep with no maintenance to help, and the astronomical cost of transport.
So if one was to be purely logical, mum chose (independently) to spend her maintenance on school fees because that's what she wanted to do with the money. Likewise OP and Husband should be able to decide what they do with their maintenance from ExW and with their extra funds now they're no longer obliged to pay maintenance because they now carry the resident parent costs.
But of course it's tricky, because no one wants to pull a Y9 age child from their school and it seems mean.
However, it seems OPs family cannot afford school fees financially, it's not pragmatic given the distance, and it's taking a psychological toll on the whole family.
It's a shitter basically. But the maintenance point is correct and relevant, because this is not a commitment that mum and dad signed up to together. It's something that mum decided to do with her maintenance money.
So the morality is different too. If the husband had agreed to all this and now wanted to backtrack that would be one thing. But he's had it foisted upon him.
If a female resident parent posted saying that her ex husband was insisting that all maintenance go towards an expensive private school she didn't choose, and she was struggling to make ends meet as a result, people would be queuing round the block saying that that's not what maintenance is for, and she must pick the school that works for her family, and ex's expensive tastes are neither here nor there unless they're prepared to foot the whole bill.
Certainly no one would countenance a resident parent mother being told to send their child to a school 90mins away by train because that's what NRP chose for convenience. And that because of that they'd get no maintenance and would have to pay half school fees and all travel costs.