Is it permissible for me to use my father's money to complete my marriage, knowing that the source of his money is from the profits of Islamic banks, and that I fear falling into temptation due to forbidden sights?

We have no knowledge of the true nature of what is happening in the aforementioned bank. However, if it conducts its financial operations according to Islamic Sharia (definition) rulings, then there is no objection to accepting your father's assistance. But if it is an interest-based (usurious) bank, and the origin of your father's money is lawful, then it is permissible for you to take from his money, because it is permissible to take from mixed funds, as long as it is not the very essence of what is forbidden, such as usurious interest.