Is it permissible for a mother to try to dissuade her own mother from showing kindness to the children of her deceased sister, due to the ingratitude of the sister's husband, or is that considered an invitation to sin?

The expenses for children fall upon their father if they do not possess wealth. The grandmother's care for them is a مطلوب (desirable and requested) matter and entails immense reward. She has the right to their custody. They should not be disliked because of their father's actions. As for the father's ingratitude and his instigation of problems with the grandmother, it is an offense, and one should be patient with him and advise him to deter him from such behavior.