My blood family is a pain

My grandma has been trying to push me to tell my blood mother about my three month old son and eventually agree to let her see him. Long story short, my mom's in prison and won't be allowed around children when she eventually gets out. I don't want to let her near him both for that reason and the fact that she broke almost every promise she made me over the years... I don't want my son to go through the pain I did of wondering if she'd call or show up. My grandma and her husband were told at the beginning of my pregnancy that I didn't want her knowing about it. It took all of two months after he was born for her husband to 'forget' (blamed it on old age + bad memory) and tell her.. My grandma has preached forgiveness to me... Am I overreacting by telling them the only way I'll allow my son to see them via vid chat is if they respect my boundary of not telling my mother about him? Edit to add, my grandma has a habit of guilt tripping me saying she won't be around much longer and wants me and my mom to fix our problems