Is it permissible to accept child support for young children from a disbelieving father? And is it permissible for the mother to ask him for additional money to cover the children's expenses, knowing that she does not take anything for herself from his money?

A Muslim is not easily judged to be an atheist or an apostate. For whoever's Islam has been established with certainty, it does not disappear except with certainty. A Muslim is not excommunicated except after conditions are met and impediments are removed. If the father is a disbeliever and his children are young and have no wealth, then their sustenance is obligatory upon him. There is no blame upon them for benefiting from his lawful wealth.