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.
If what you mentioned is confirmed that your father deserted you and your mother all this long period without a sound reason, while your mother is still his wife, then he is very wrong. ‘Abdullaah ibn ‘Amr narrated that the Prophet said: “It is enough sin for a person to neglect those who are under his care.” [Ahmad and Abu Daawood]
However, since your father came to apologize to you, then his children should accept the apology of their father. Al-Hassan Al-Basri said: 'If someone insulted me in one ear and apologized to me in the other ear, I would accept his apology.’ Besides, Al-Ahnaf ibn Qays said: 'If a person comes to you apologizing, then welcome him with joy.' If this is in regard to the general people, then this is more confirmed in regard to the father.
Indeed, those children should know that they are obliged to be kind and dutiful to their father and obey him within what is permissible. His mistreatment to them is not a sound reason for them to disobey him, because Allaah ordered us to be kind and dutiful to our parents even if they are non-Muslims and even if they try to lead us astray, let alone if they are Muslims. Allaah Says (what means): {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 31:15] For more benefit, please refer to Fatwa 87019.
As regards not going to see him in your aunt’s house when he asked you to go to see him there, then if there is no sound reason for you for not going there to see him, then you are wrong for not going because you are obliged to obey him within what is permissible. The fact that you heard that he supplicated against you is not a sound reason for disobeying him. Moreover, he might be embarrassed for being negligent towards you in the past and it is for this reason that he did not come straight away to your house.
Nonetheless, it is not permissible for a parent to supplicate against his/her children without right, and we hope that such a supplication is not answered because it is reported in a an authentic narration that the Prophet said: "The supplication of a person is answered as long as he/she does not supplicate for a sin, or for the cutting of relations with kinship." [Muslim]
As regards your mother, you are also obliged to be kind and dutiful to her and obey her within what is permissible, but if she orders you to do an act of disobedience, then it is not an obligation to obey her, like when she orders you to stay away from your father, so you are not obliged to obey her in this.
Besides, you should be wise about how to keep ties with your father with the means of keeping ties with him, but you should not anger your mother, especially that she is sick as you mentioned; for more benefit, please refer to Fatwa 97282.
Finally, it should be noted that your father is not permitted to leave your mother like this hanged [neither married nor divorced]; he should either keep her in kindness or divorce her in kindness. Therefore, your mother may take her matter to the authorities who are responsible for the affairs of the Muslims, like the Islamic centres so that they would study her case and repel the harm off her.
Allaah Knows best.