Is a person considered a dayyūth if his mother uncovers her hair in front of a non-mahram man, thinking that he is still young, and what is the repentance for that?

It is impermissible for a mother to go out with her head uncovered while accompanied by her son who is fifteen years old or older. A Dayyūth is one who lacks ghīrah (protective jealousy) over his family. You must admonish her respectfully and gently. If you do so, you will not be a Dayyūth.