I've thought of something similar!
If Max and the Duke were as close as this timeline and working together then it might be possible that Max only went in there to guard the princess and fill her in on what was actually happening since it states that only those of royal bloodline can enter and exit as they please meaning her father couldn't go inside and do that himself. Also the Duke had said 'it isn't the time yet' when thinking of overthrowing the King so I think 'the time' was when he made a move against his daughter by blaming her of the poisoning. Meaning he probably went batshit and killed everyone after MC died.
I'm sure he also acted cold towards MC bc he didn't want her to be found out as his weakness, though that didnt end up mattering. In the end her death came about because he wasn't able to be a parent who could at least communicate with her :/
And seeing how her memories didn't return until 2 years after she started dating Mc Douchebag, it would only make sense for their relationship to be the same since the crown prince said he was training with her dad for over 10 years which is well before her memories returned. Communication could fix the vast majority of the relationships in these stories but where would be the fun in that ╥﹏╥
So this is just a theory but....
What if her father's feud with the king is the reason why she was framed in her past life? They mentioned that the king only sees his children as pawns so it isn't too far-fetched if the king wanted to bring down the duke's reputation by poisoning the princess and trying to frame it on the duke's daughter (our MC).
Another similar theory is that it was Max (the crown prince) who wanted to push the duke to rebel by using his daughter's false imprisonment as grounds. Max was cast away by the king because of his mother (the dead empress) but the princess seemed like she was raised in the palace, meaning she was a concubine's child and she grew up separately from Max. Given the grudge that Max holds for the emperor and his whole stance on family and love (how it's a useless weakness), it would also be possible for him to sacrifice the princess in order to get the duke to make a move. That could've been the reason why he was heading to the MC's cell in the original story (to fill her in on everything) and why he was so shocked when she stabbed herself in front of him since it wasn't his intention for her to kill herself and he never intended to torture her -- he could've just wanted the guards to move so he could have a private conversation with her about their plan to overthrow the current king.
Just a theory and I do tend to overthink but I think it'd be cool ╮(￣▽￣)╭