The premise itself feels a little forced - we're told right up front that husband is cheating and plans to fake a bastard as the legitimate child. But given the context of the husband being a commoner who clearly neglected to learn about being a noble (nevermind attending to the duties of running the estate) while his wife has always been more knowledgeable and well-connected, it's a bit hard to just nod along and go "yes, she would have trouble arranging a divorce". And that's without any of the events later in the plot.
I've gotten a ways into this and it's a little refreshing so I don't mind overlooking my usual qualms about internal consistency. Most stories of this nature that hinge on noble etiquette and standing and all that, they usually dunk on the nobles. It feels a little new seeing this coming the other way, with the commoners being the antagonists, with many being dumb but some being cunning. It still feels like a forgone conclusion but I kinda look forward to seeing how MC will judo the dumb family into humiliating themselves while realizing they are more to blame than she is.
If there is one thing that bothers me after all of that, it's just that MC really doesn't seem to take into account a plan in the event the dumb family becomes truly violent. Sure, she doesn't know the scope of how far they might fall but she's got to be aware of what they would be willing to do if her plan actually works. As the reader, I'm confident the author will have a plan for that, but it bothers me that someone who otherwise seems intelligent is neglecting such an important point.