What is the ruling on the exchange of sexual words and images between engaged couples over the internet, what are the consequences of that, and how can one repent and have it accepted by Allah?

Lenience between a man and a non-mahram woman, and conversations that are not subject to Shariah controls, are a gateway to corruption. What they did is a reprehensible act. The family's knowledge does not legitimize this; rather, it is a form of dayouthah (pimping/cuckoldry). They must sever the relationship completely, abandon the conversations, and perform sincere repentance. Allah forgives those who repent, believe, and do righteous deeds.