Don't mean to put a stop to your parade but he didn't do any of that...,......
Spoiler
He died without marrying and the kid that is mentioned is a distant relative that was adopted cause he didn't get married or have kids. Maybe it's a big shock but the fiance lied.
Also from what the novel showed, it will be explained. It will take a while though or else this story would end too soon as it seems like their relationship is the true bulk/ plot of the book so it's drawn out a bit. BTW he did try to explain the ml just didn't want to hear it so it was never resolved when he tried.
At first I though the prince was innocent but now idk he had a child or a few with that evil b*ch and also and purposed to her. Even if it was arranged and forced to do it and stuff you could've at least explained it to her seeing as you are reincarnated but instead of that you chose tell her to sweep what happened under the bridge and into the water without so much as an explanation of to why I've seen spoilers and sure hope they don't get back together if it is not explained. There'd better be a good reason cause I swear if there was no reason or even a good reason for his actions I'm dropping this.