All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we would like to say that your mother is very wrong for abandoning the prayer and keeping company with bad people. She is also wrong for seeking to sow hatred in your heart towards your father. However, you should not forget that she is your mother; although she is wrong, you are still obliged to be kind and dutiful to her. Among the best means of being kind to her is to supplicate Allaah to guide her and turn her into a righteous person, and you should advise her with wisdom and good admonition.
Indeed, you did well by contacting your father after this long period of cutting ties with him. So, you should repent to Allaah for this and endeavor to be kind and dutiful to him in the future.
You are not permitted to obey your mother when she orders you not to keep ties of kinship with your father, as there is no obedience to a creature in disobeying The Creator. Therefore, it would be wise to continue keeping ties with your father without the knowledge of your mother as a way of combining between the benefit of keeping ties with your father and not angering your mother.
For more benefit on the right of parents in being kind and dutiful to them, please refer to Fataawa 87019 and 84942, and also to Fatwa 85878 about the position of children when parents differ or separate.
Finally, if you are afraid of being tempted (into wrongdoing) by staying with your mother, it becomes permissible for you to move to live with your father. It might even be an obligation upon you to do so even if your mother becomes angry because of this. Moreover, some jurists are of the view that the husband has the right to foster his daughter after the age of seven until her wedding to her husband, because her father will protect her better and he has more right to be her guardian. For more benefit, please refer to Fatwa 95996.
Allaah Knows best.