Is it permissible for a charity sacrifice to be offered on behalf of the grandmother with the mother's money and the mother's intention, given the absence of the sacrificer at the time of slaughter despite his having purchased the animal and taken it to the abattoir?

Not witnessing the slaughter does not affect the intention. If you intended the charity on behalf of your grandmother, then deeds are judged by intentions, and presence or witnessing is not a condition. If the conditions are met and the impediments are absent, then the благотворительность is accepted, Allah willing.