I used to run a will-writing company, so I can provide some information here but not, regretfully, a definitive answer:
1. A well-written will should specifically state what should happen if one of the beneficiaries dies before the testator. So, if such a term exists within the will, then the wording of that term will come into effect.
2. Where there's no relevant provision in the will, the death of a childof a testator can see their inheritance pass 'downwards' to their own children but not 'sideways' to their spouse. There are no other 'automatic' allocations of part of an estate which would have gone to a deceased beneficiary, so the wife of the deceased grandchild can't inherit under the terms of the will.
3. Where the absence of any specific provision, as referred to in paragraph (1) above, applies and there's also no 'automatic' allocation, as per paragraph (2), then the will needs to be examined to see whether a 'residuary beneficiary' is named. (e.g. "I give everything else to Fred Bloggs"). In which case, depending upon the exact wording of the will, it's possible that the residuary beneficiary might inherit what should have gone to the deceased grandchild.
4. It's more likely though that there will simply be a 'gap' in the provisions of the will, meaning that a 'partial intrestacy' will be created. That means that the unallocated part of the estate would be dealt with as if the testator had died without leaving a will. In this case it would mean that the unallocated sum would pass to the testator's daugher (or, if she's got other children as well, equally between all of her children). [I've assumed that Grandma's husband is no longer alive].
As Grandma is still alive she really ought to amend her will to cover the new circumstances. A simple codicil, along the lines of the following, is all that's required:
"This is the first codicil to the will dated _________ of me Granny Smith of 23 Acacia Avenue, Sometown in the county of Duffshire.
1. I revoke my gift of one sixth of my estate to John Bloggs.
2. I revoke my gift of one sixth of my estate to Freda Bloggs.
3. I revoke my gift of one sixth of my estate to Simon Bloggs.
4. I give one quarter of my estate to Freda Bloggs.
5. I give one quarter of my estate to Simon Bloggs.
6. In all other respects I confirm my will.
Date:
Signature:
Signed by Granny Smith in our presence and then by us in hers:
[Signatures of two witnesses, preferably with their names and addresses printed below them]"