How can children absolve themselves from the sin of their father's usurious dealings, which have negatively impacted their lives, especially since they tried to convince him without success?

We advise you to continue counseling your father and explaining the impermissibility of usury (riba) and the enormity of its sin. If you fulfill your duty of advising, then there is no sin upon you for what your father does, as Allah Almighty says: "And no bearer of burdens will bear the burden of another."

Regarding benefiting from his money: If he borrows with usury, there is no harm for you in benefiting from his money, because the impermissibility of a usurious loan pertains to the borrower's responsibility, not to the loan amount itself.

If he lends with usury and also has another lawful income, then his money takes the ruling of mixed wealth, and you are permitted to benefit from it, though it is disliked. However, if all his money is unlawful, then it is not permissible for you to benefit from it except in cases of inability to earn a living.