Is it permissible for a father to prepare his daughter for marriage and marry off his son before paying off a large debt he owes, knowing that they live a comfortable life and own a luxurious car, and will Allah bless them in that?

If a debt is due, it is obligatory for the capable debtor to pay it promptly, because "the procrastination of the rich is injustice."

Therefore, it is not permissible for your father to prioritize spending on your dowry or your brother's marriage over settling his due debt, because the preponderant opinion is that fathers are not obligated to marry off their children. Similarly, it is not permissible for him to spend money on things that can be dispensed with, as long as his wealth is insufficient for both expenditures simultaneously.