hate they treat everyone else with?
I am not sure its hate in many cases it a sense of entitlement. However the answer is YES If they are the malignant type. They pick on the vulnerable - children. How do you think we had horrific abuse that took place in children's homes, in schools and mother and babies homes, and in homes in the past? Regarding the narcissist's own children they can scapegoat the emotionally strongest child because that child will try to stand up to them and often can see through them. Or a child or grandchild can be also love bombed because they are being groomed for abuse (emotionally, physically, sexually). This helps the narcissist get control and helps to silence the child who does not understand the dynamics at play. They will play children against children and children against mum or dad, whoever is not the narcissist. The narcissist can be male or female. This causes divisions and triangulations in the family I.e. a child getting more attention then the mother or other children. Relationships will be affected and it will be not fully understood why? Because everything is kept a secret and the abused child is afraid to disclose what’s happening and often blames themselves. The narcissist see their children as an extension of themselves so its like it's their right to behave as they wish and they do not question their behavior. In my work I have also noted as they become grandparents they can also pick on the nice or vulnerable grandchildren and the pattern continues. So I would encourage that children are supervised closely or kept away from these narcissistic grandparents because they have their favourites and are not consistent caretakers. Children must be protected from this type of person because the consequences of not doing so remain for life.