All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If your father mistreated you and your mother as you mentioned, then there is no doubt that he is very wrong and very unjust. However, he remains your father; his mistreatment does not relieve you from the obligation of being kind and dutiful to him. Allah did not invalidate this obligation even towards a non-Muslim father, let alone a Muslim one. Allah 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]
Al-Bukhaari wrote a Chapter in his book Al-Adab Al-Mufrad which he entitled "Chapter: Dutifulness to Parents, even if they are unjust." In this chapter, he mentioned a statement by Ibn ‘Abbaas in which he said: "Any Muslim who has two Muslim parents and he obeys Allah regarding them, Allah will open two gates of Paradise for him. If there is only one parent, then one gate will be opened for him. If he makes one of them angry, then Allah will not be pleased with him until that parent is pleased with him." It was said, "Even if they wronged him?" He replied: "Even if they wronged him."
Indeed, you have done well by taking care of your father when he was sick –may Allah accept this from you. All of his children are obliged to contribute to his care –each according to his condition –so this is not an obligation on you only.
Moreover, you are not allowed to leave him unattended in a manner that could endanger his health (or life), for as long as he needs care.
If you leave him in his house, then you should hire a trustworthy person, who would take care of him, and who would be patient with him and serve him; you should visit him and check on him from time to time.
However, your mother has no right to prevent you from fulfilling your obligation towards him, and you do not have to obey her in this regard if she prevents you from being kind to your father, because obedience is only in what is (Islamically) permissible.
For more benefit on the limits of obedience to parents, please refer to Fatwa 131695.
Regarding your father claiming that you are not his son, if he intended to deny your descent from him, then this is a great evil. Abu Hurayrah narrated that the Prophet said: "Any man who denies his son (to be traced back to him) while looking at him (knowing that he is), Allah, the Mighty and Sublime, will deprive him (the father) from looking at Him (Allah) and disgrace him before the first and the last (of creation) on the Day of Resurrection." [An-Nassaa'i and Abu Daawood]
This may also include another prohibition, which is accusing your mother of adultery. This makes him deserving to receive the Hadd (the corporal punishment imposed by Islamic law) for falsely accusing someone of adultery. Allah Says (what means): {And those who accuse chaste women and then do not produce four witnesses - lash them with eighty lashes and do not accept from them testimony ever after. And those are the defiantly disobedient.} [Quran 24:4]
To conclude, we recommend that you seek the help of some people who are close to him to advise him and remind him to repent to Allah for neglecting the right of Allah Almighty, and the right of the creation, hoping that Allah will enable him to repent.
We also advise you to forgive him and pardon him so that he will not meet the consequences of his wrongdoing to you [on the Day of Judgment]. Forgiveness is a great means of being reward by Allah. Allah Says (what means): {…but whoever pardons and makes reconciliation - his reward is [due] from Allah.} [Quran 42:40]
For more benefit, please refer to Fatwa 97282.
Allah knows best.