OP, you say that your DF valued education but 'wasn't able to fulfil' this for you and your DSis. What exactly does this mean? Do you mean he couldn't afford private school for both of you, or that you both ended up going to shitty schools and not fulfilling your academic potential?
Also, what was the family dynamic between you, DSis and DF when he was alive?
Ignoring the legal side, it sounds as if your DSis may not have had the ideal education herself, wants to get it right for her kids, but feels she is being told she can't afford it because both her parents favoured you and your children and she can only watch as her offspring also do not achieve their potential.
I understand there are all kinds of factors at play and the above may not be the fairest interpretation, but I don't think this is really just about money. It's about 'who did Dad love more?' I don't think your DF could have anticipated this situation so it isn't fair to say he didn't love you both equally, but when we think about our parents, we naturally fall back into the viewpoint of a child, and then when you throw grief into the mix, being rational becomes quite difficult indeed. I know it's been a while and she's always been quite self-sufficient, but I don't think it's unreasonable to suggest she may not be over becoming an orphan.
Suggesting you pull your kids out of school isn't a fair response, but it's an understandable one after you've told her how you've spent the best part of £135k and there's nothing left for her kids. It's a panicked reaction born out of a place of trying to protect her kids.
Having put yourself in her shoes, the question is what do you do about it.
Firstly, could you have done anything if you wanted? You've dodged the questions about the legal wording, which would really clarify whether you had any input into how the will was spent, or if the money really did have to be ringfenced for your children.
Secondly, if you were in her shoes, what would think was fair?
It may be worth writing your sister a letter (an email or text will do) and explaining that the money was specifically left to your children (if that is true) and that you legally cannot share that money with her children, but you understand why she is upset and you're very sorry no one anticipated she would have children of her own when DF was drawing up his will. Say that you love her, your kids love her and you know that DF really loved her too - you want to make this right, but you don't know what to do given the legal restrictions at play.
With a bit of distance to cool down and read your message in her own time, she may be able to come up with a better suggestion than take your kids out of school. Acknowledge her hurt and take it from there.
I really hope you can salvage the relationship.