My grandmother possesses any legal authority to allocate this property to specific children.

Your grandmother is having a right in common over the property insofar as her share alone in the property.

She is one of the shareholders in the property.

She cannot decide about allotting any property to anyone.

She can get her share separated from the property and can dispose that alone in favour of her chosen person.

First thank you so much for your prompt reply👍

is she holding any power to write any WILL etc ??

Your grandfather's all legal heirs ( your grandmother,and four children) are entitled to get equal share and rights in property belonged to your grandfather .your grandmother can't give the property to her particular child however she can claim partition of property and can bequeath her share to particular child.