Hi, thanks for your enquiry.
The Wills Act Section 33(1) provides that:
a) ‘where a will contains a devise or bequest to a child or remoter descendant of the testator; and
b) the intended beneficiary dies before the testator, leaving issue; and
c) issue of the intended beneficiary are living at the testator’s death,
then, unless a contrary intention appears by the will, the devise or bequest shall take effect as a devise or bequest to the issue living at the testator’s death’.
For example, Tom gifts the residue of his estate to his two sons in equal shares. The eldest son Peter dies before Tom, leaving two children. Section 33(1) Wills Act operates to ensure that the two grandchildren of Tom (Peter’s children) take Peter’s half in equal shares.
Although it is not possible simply to exclude the doctrine of lapse under a will, the testator may of course provide for an alternative in the will so that another legatee or beneficiary takes the gift instead. This could be done by a substitutional gift. So, in simple terms, provided your Grandmother's Will SPECIFICALLY states that the share of any predeceased child should pass to someone else other than the grandchildren, you will inherit your Mother's share and not her siblings.
I hope this assists and sets out the legal position. If so, I would be grateful if you could rate my answer.