You husband's grandmother cannot dictate how you, he and his ex-partner choose to educate their and your children.
For a start as pointed out above private education for 4 children is likely to cost from £40,000 per year upwards and that doesn't include the cost of uniforms, school trips and extra-curricula activities such as music lessons. Even assuming the children are only privately educated through secondary school then you are looking at a minimum of £280,000 required. Is the net estate large enough to support this cost ?
What happens if the children don't get into a private school ( most are selective) or are unhappy there ? How old are the children and the grandmother ? My grandmothers both died after I had left both school and university. My husband's grandmother is still very much alive and he is 38 ! What happens to the money in those circumstances ie if the children are too old for education by the time she dies?
What happens to the money if the children are not privately educated ? Who gets it ? Was the will professionally drafted or is it homemade ?
It seems a very odd will to make if I'm honest. I could understand if she was already paying for their education and wanted to make sure that this continued after her death to provide some stability for the children, but this will seems to do the exact opposite of that. She seems to be saying that when she dies she wants all 4 kids to be pulled out of whatever school they're in at whatever point in their education ( mid-GCSE year for example) and be sent somewhere else. How is this supposed to be beneficial for them ? If private education is so important to her why isn't she funding it now ?
Anyway, after all that, in answer to your query you will not get into any kind of immediate "trouble" for not carrying out her wishes. Generally trusts are fairly widely drawn to allow the trustees power to deal with a variety of family circumstances. If the trust specifies that the money can only be used for school fees then presumably there must be a default clause that says what happens to it if either a) the children are too old for education or b) private education didn't happen. In this case you would just distribute the funds as per the default clause. The only issue is that in theory your own children could sue you as adults for breach of trust if they believe that they have been disadvantaged by your actions. Only you know how likely this is to happen and it would be a very difficult case to prove.
You may wish to consider resigning as Trustees when the time comes and appointing professionals in your place as I think you could have a conflict of interest in these circumstances as both Trustee and parent ( particularly if the money goes to say your DH if the children don't go to private school). I would suggest that if you have a copy of the will you take it to a solicitor and get some proper legal advice if you are concerned.
And as an aside if I were your DH's ex there is no way on earth that I would allow my ex-MIL to dictate the terms of my children's education.
PM me if you want any more help.