Well this is an isekai so I'm not expecting much from the story, but if a manga is trying to get me invested by putting me through tragedy (as opposed to other isekais that are basically power trips), I'm only willing to susoend disbelief so far.
The family didnt believe her to be the murderer yet still sold her to slavery? Uh, if the father of the victim says its ok, they wouldnt need to enslave her right? Fiiiiine, maybe the family is pressured by other nobles to do so.
Then, why her horrible treatment in jail? Cant they just shove her in a separate prison under the guise of "extra security" while actually treating her decently? Fiiiiiine, maybe her bad condition is mostly caused by her own grief and self-deprecation. No matter how well you're treated, refusing to eat much for months will fuck you up.
I cant however think why the family would let the owner of your son's killer to stay in your mansion as guest. It shows to whoever's pressuring the family in the first place that the family doesnt hold much grudge for the slave girl.
I can only suspend my disbelief so far, especially if the author dont even acknowledge these emotional plot holes