Private education for two kids at a decent day school all the way up to 18 can cost £500-600,000, or nearly £1m before tax. Even for the sorts of people who live round nappy valley that's an enormous commitment. If it were for some life saving medical treatment then I'd understand where you were coming from, but private school fees really isn't one of those things.
Also, don't underestimate the huge resentments that this may bring up further down the line once the divorce is ancient history, and say the kids are unruly teenagers skiving lessons, or seemingly squandering the opportunity your husband has given them. That could be terminal to your relationship with your sister
Sure it would be nice to help out with this year's fees so the kids aren't taken out of school mid term, especially if your sister is just waiting for her ex-husband to sort out maintenance payments. That's the sort of thing all families do for each other. But thereafter it's hardly a catastrophe if they end up going to state school thereafter. 96% of the UK population manage fine, and tens of thousands of families go through precisely the same experience of tighter family finances after after a divorce. Kids are pretty resilient about this sort of thing.
If you are determined this is the right path forward, can I suggest you try to put yourself in his shoes. Would there still be sufficient money left for him to make a similar gesture if, say, the same thing happened to his siblings a few years in the future. And would you mind if all the roles were reversed in the situation? It's probably just me being fairly selfish as a man, but it feels like a huge financial commitment to protect the kids from something which - in time - will not be disastrously awful.
Everyone has different approaches to money, and none of them is necessarily the right one. Personally I wouldn't sign my kids up to a private school without knowing I had a few years fees inreserve to protect the from precisely the disruption of divorce or job loss. I slightly sympathise with your husband feeling that those (especially who've not had a rough start in life) have to live with the consequences if they choose to live a bit more on knife edge. Again we clearly not talking about a family living on the breadline here
When I was growing up my parents paid for private school fees but money got very tight in later years. My uncle was loaded and could easily have helped, but not for one moment do I think it would have been appropriate for him to pay - intact it would have made for a very awkward relationship with him thereafter. In reality, being told I had to win a scholarship and that we wouldn't be able to take any holidays for a few years was a very useful lesson that life is rarely easy but dealing with those challenges is what living is all about