Is the non-acceptance or unanswered nature of a prayer contingent upon spending money from a father who sells tobacco alongside other permissible goods?

There is no sin upon you for spending from your father's money or taking from it for your needs, as long as his money is mixed (with lawful and unlawful) or even if it is entirely unlawful. The apparent dominant characteristic of his wealth is lawfulness, so there is no harm in you taking from it. Your supplication, God willing, will be answered, as you do not consume unlawful wealth. So, strive in supplicating for his guidance and continue to advise him gently.