My maternal grandmother died recently and she was a Kafir and only my mother among her children is a Muslim. She died and left a lot of wealth without a will. The Kenyan secular law states that all the surviving children are lawful inheritors and all of them have to avail themselves to the relevant authorities for division of the deceased's wealth and if one child refuses to attend then the rest can't receive their share. Is my mother legislated by Islamic law to accept her share? Please advice with evidence. What options does she have in whatever Islamic ruling given?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
A Muslim can not inherit from a Kafir relative nor can a Kafir inherit from his Muslim relative for the rule of the Prophet who said: "A believer can not inherit (anything from an) infidel and an infidel can not inherit from a Muslim". [Reported by Imams Bukhari and Muslim]
Therefore, your Muslim mother does not inherit from her non-Muslim mother. If the authorities will not give the other inheritors their share till your mother accepts also then make it clear to them that she will never take her share because of her religion's teachings. If they do not agree and insist on giving her a share then she may receive it only to give it to other inheritors but not to use it herself.
Know that everyone, who leaves something solely for the Sake of Allah, surely Allah will grant him better than what he has left.
Allah knows best.