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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
First of all, we say that consuming a person's mixed wealth (i.e. his income comes from both lawful and unlawful sources) is not prohibited; rather, it is disliked, as explained in Fatwa 90278.
It is your husband's duty to provide for you. The husband is obliged to provide maintenance for his wife as Muslim scholars have stated. Please refer to Fatwa 85361.
It is strange that the husband neglects fulfilling this religious obligation under the pretext of working in Da‘wah. This is certainly not a valid excuse. The Prophet, sallallaahu ‘alayhi wa sallam, the Imaam of all the preachers and the role model for Muslims, was never preoccupied with Da‘wah to the extent of neglecting his wives and not fulfilling his duties toward them. ‘Umar narrated that the Prophet, sallallaahu ‘alayhi wa sallam, used to sell the dates of Banu An-Nadheer and store for his family food that would cover their needs for a year. [Muslim] Please refer to Fatwa 101108.
Based on that, your husband should be advised to fear Allaah and strive to work and earn a living to provide for his family. He should be informed of the gravity of neglecting the fulfillment of that religious duty and the stern warnings reported about this. The Prophet, sallallaahu ‘alayhi wa sallam, said: “Suffice it as a sin that a man neglects his dependents.” [Abu Daawood]
If your husband does not provide for you, then he has no right to prevent you from going out to work in order to earn a living if you are in need of it. Also, he has no right to prevent you from accepting your father’s gift from his "mixed money" even if you are not in need of it and he is providing for you adequately. He may only advise you not to accept your father’s mixed money out of piety if you are in no need of it.
Allaah Knows best.