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 is His slave and Messenger.
First of all, you should know that no matter to which extent your father is wrong, he remains your father, and you are obliged to be kind and dutiful to him. The children are obliged to be kind and dutiful to their father under all circumstances because Allaah ordered us to be kind and dutiful to the parents even if they are non-Muslims and try to lead their children astray. Allaah says (what means): {And We have enjoined upon man [care] for his parents. His mother carried him, [increasing her] in weakness upon weakness, and his weaning is in two years. Be grateful to Me and to your parents; to Me is the [final] destination. But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness.} [Quran 31:14-15]
The family of your mother were correct in advising you to uphold the ties of kinship with your father. Hiding your ties with your father from your mother is not considered cheating her; rather, it is an act of righteousness since by hiding it from her you respect her feelings and avoid making her unhappy. For more benefit, please refer to fataawa 89630, 186843 and 132640.
Besides, your mother has no right to prevent you from upholding the ties of kinship with your father, and you are not sinful if she came to know about it and felt hurt. If we presume that she were to cut ties with you because of this, then she would be the one who was sinful and not you. However, you should try to please her. Just as your mother and her family have a right upon you to keep ties with them, your father and his family also have a right upon you to keep ties with them.
Moreover, the fact that the family of your father commit innovations does not prevent you from keeping ties with them. However, if you fear any harm by visiting them, then you may contact them and ask about them through other means of communication. Keeping ties depends on the customs. They should be advised and their innovations should be rejected. One may seek the help of some scholars and preachers, hoping that they would be able in rectifying them.
The most important thing that may lead to solving the problem is to reconcile between your mother and your father and his family. Allaah says (what means): {No good is there in much of their private conversation, except for those who enjoin charity or that which is right or conciliation between people. And whoever does that seeking means to the approval of Allaah - then We are going to give him a great reward.} [Quran 4:114]
Abu ad-Dardaa’ narrated that the Prophet said, "Should I not tell you about what is better than the degrees of fasting, prayer and charity?" They said, "Yes." He said, "It is to reconcile between people, for spoiling relations between them is the shaver (the destructive)." [Ahmad and At-Tirmithi] The shaver' means that which destroys one’s religion.
According to what you mentioned, it does not appear to us that you are responsible for what happened, and you are not obliged to believe your mother if she claims that her husband's family have wronged her. The Islamic rule that applies here is to verify the information, as Allaah says (what means): {O you who have believed, if there comes to you a disobedient one with information, investigate, lest you harm a people out of ignorance and become, over what you have done, regretful.} [Quran 49:6]
In conclusion, we remind you to be patient, as this is one of the greatest causes for finding a way out of your difficulties, and you should be keen on mentioning Allaah and seeking His Forgiveness; Allaah says (what means): {Those who have believed and whose hearts are assured by the remembrance of Allaah. Unquestionably, by the remembrance of Allaah hearts are assured.} [Quran 13:28]
You should also strive in supplicating, as this is a strong weapon in facing difficulties and removing adversity. Allaah says (what means): {Is He [not best] Who responds to the desperate one when he calls upon Him and removes evil and makes you inheritors of the earth? Is there a deity with Allaah? Little do you remember.} [Quran 27:62]
Allaah Knows best.