OP, please stop feeling bad. It was never your money to give away.
The reality is that your sister, as an intelligent woman, must be aware that money left in trust to minors cannot be diverted to the benefit of anyone else. That's completely against the law, and they could actually sue for breach of trust if any such diversion occurred. It's an absolute non-starter. Her assumption that she could just help herself to their inheritance for the benefit of her children is pretty fucking stupid. As is the belief that the pot would fund anyone's kids through private school from Reception to 6th form.
What was your sister expecting? That you'd not spend the money, despite your dad specifically setting out the terms of the bequest as being for the education of your children, in the hope that at 18 you could pressure them to sign half over to her kids? Is she aware that they would have every right to refuse to do that, at that age, because it's their money? And there would be precisely nothing you or she could do about that?
She's been looking at private schools that start next year, when your kids are four years away from being able to sign away anything, even had they wanted to. And your kids went to private secondaries, anyway. There was never enough money in that pot to privately educate four kids through secondary school, far less all through, so she's living in cloud cuckoo land on many fronts. Not your money to give her; even if it were, not enough for what she's planning.
Your sister has simply chosen to believe what suited her, and is now very angry when reality is knocking. Is it fair on her kids? No, of course not. Is that anyone's fault? No. And it can't be adjusted now.
Was it a badly drafted will? Yeah, possibly. The other possibility is that your DF knew more grandchildren were unlikely, but he also loved the ones he knew, and really wanted them to get this start in life. He left them hugely more than he did his own daughters, after all. It could well be that his personal love for them meant he wouldn't have wanted it split between grandchildren he would never know - that he left it to the grandchildren he loved and who made his last years happier, and not to, "the grandchildren" as a concept. There's no means to tell, but you and your sister aren't entitled to decide to disinherit beneficiaries of his will, because your relationship with one another is your priority. His will. Not your call, nor hers. You can't know what his thoughts were. All you can know is what the realities are.
It's a shame and very hard on the cousins, but let's be clear: two working parents, with a large-ish house, yes? Presumably with a lot of equity? Far more attention because there are two adults to provide it? Whereas your kids are living in a smaller house, and have a single mum? That's not equal, either. Life isn't. Sometimes the breaks aren't equal. But expecting your kids to hand over money they actually need to get through uni, to a family who are better off, is unreasonable IMO. Your sister does seem rather to feel that heads your kids should lose, and tails her kids should win. And if you re-mortgage, then you're agreeing with her.