Is ironing clothes with an electric iron instead of the iron used by the father considered cheating, and is the money earned from that unlawful (haram), and what is the correct action to take in this situation, and is it permissible to use this money given that the father is the family's provider?

If customers request that clothes be ironed with a charcoal iron, it is not permissible to use an electric iron without their knowledge, because that is a forbidden deception, and "whoever cheats is not of me." Money resulting from deception is forbidden, and the parents must repent and dispose of it. It is sufficient for the father to clarify that he sometimes uses an electric iron, either by a sign or by making the ironing with it apparent. As for whoever stipulates ironing with a charcoal iron, it is not permissible to go against his condition. There is no harm for you in benefiting from your father's money even if he continues to cheat; for money that is forbidden to earn is only forbidden for its earner, and if your abstention from benefiting from it helps him abandon cheating, then do so.