(2-part post):
I also think that, for a definitive answer, we might need the services of AB's helpful barrister, Barmaid. While I used to draft wills for a living, my knowledge is mainly associated with 'getting it right', rather than with what happens when things go wrong.
However, my understanding is that when a beneficiary signs a will it only removes their entitlement to receive any specific legacy from that will. It does not, per se, remove their entitlement to inherit from the estate.
Where a will 'leaves a hole' by not making it clear to whom a certain part of the estate should be given, that part of the estate is dealt with as if the deceased person had died intestate. In this particular case, it seems that the whole of the estate should now be distributed according to intestacy law. In the absence of a surviving spouse, that means that the two children of the deceased will each get half of the estate. (That might result in exactly the same outcome as if the will had been properly witnessed but not necessarily so. For example, the will might have sought to distribute the estate on a 70:30 basis, rather than 50:50).