Is it possible to be content with a formal relationship with a father who curses the religion, disbelieves, and slanders, especially after he disowned the questioner financially and morally?

If what is attributed to the father is true, then it is an act of disbelief that expels one from the fold of Islam. However, this does not preclude associating with him kindly and maintaining ties with him, in compliance with the Almighty’s saying: ﴿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 kindness.﴾ [Luqman: 15]. You must call him to repentance and gently and kindly explain the gravity of his action. What you claim regarding his slander against you does not negate his rights.