Is money earned from the father's work in an interest-based bank considered unlawful money, and does that affect the validity of the worship of the children and wife, and is the daughter sinful for eating, drinking, and being educated from this money, and can difficulty in marriage be due to this money?

The father's work in a usurious bank is forbidden (haram), and he must repent and leave it immediately, unless he is compelled to it, such as not finding any other work or needing to repay a debt. As for the daughter, she must search for a permissible job to become independent of her father's money. If she does not find one, there is no sin in taking the money due to necessity. The prayer of someone involved in usury is not invalidated, for a bad deed does not nullify a good one.