Is it permissible for a father to disinherit his son merely because he divorced his mother, or for other reasons?

The heir is determined by Islamic law, not by the parents' wishes. A son is an heir by consensus, unless there is a legal impediment. The impediments to inheritance are: murder, slavery, and difference of religion. The father does not have the right to disinherit his son, nor does the father's divorce of the mother prevent the son from inheriting.