Is advising the mother to stop chatting with young men via Facebook sufficient to remove the description of "dayouth," and what is the necessary advice in this situation?

As long as you have forbidden your mother from evil, you are far from being a dayyuth (one who tolerates immorality in his female family members). Your duty is to continue to forbid her from evil and warn her against following the footsteps of Satan, while trying to prevent her from the causes of corruption as much as you can. This must be done with gentleness and reverence towards her, for enjoining good upon a mother and forbidding her from evil is not like doing so with others. Rather, it should be done by teaching her, without violence, abuse, or harshness in speech.