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 is so poor that he could not earn his living, you should first discuss the issue with your sister and perhaps she could be able to spend on him. If your sister achieves that goal, then this will spare you from getting into conflict with your husband. Now, if this solution is not possible, then try to convince your husband either to permit you to work in order to spend on your father or if he is wealthy, he commits himself to spend on your father and assures you that he would not break his commitment. Now, if none of the above solutions is reached, then two obligatory acts, spending on one's father and obeying one's husband, conflict. In this case, if your quitting your job will make your father face much hardship and difficulty, then the right of the father is given priority over that of the husband. As a result, you should not obey your husband in this particular issue as the Prophet said: “No obedience is due except in a righteous deed.” [Al-Bukhari and Muslim]
We would like also this husband, in case he reads this Fatwa, to be a supporter for his wife in obeying her Lord by obeying her father, considering that she might also become the mother of his children if Allah Wills.
Allah knows best.