Is it permissible for a wife to seek divorce from her husband who drinks alcohol, talks to women, does not pray, and mistreats her and her family, especially since she has a young daughter?

If the husband is as described—neglecting prayer and drinking alcohol—he is derelict in his duty to his Lord and unjust to his wife.

Originally, it is not permissible for a wife to leave her husband's home without his permission, except for a legitimate religious reason, such as averting harm from his aggression against her. If she has no such excuse, she must return to her home and advise her husband. If he repents, then praise be to Allah. Otherwise, she should seek a divorce. She is not obliged to obey her father if he prevents her from seeking a divorce, for "obedience is only in what is right."