First of all...what a horrifying thread..Yikes! So many murders around the world? Scary!!

Flor: A man should inform his existing wife/wives if he intends on taking another. This is of good and virtuous manners manners and Islam always promotes fairness and care for another specially in marriage. The wife then has a choice to either stay married to the man or divorce him. And the man can then decide(if she chose the latter) if he actually prefers to lose his first wife over his want for another. Oppression,abuse,and betrayal are never a good thing in any marriage in Islam be it your first or third. A man can have more than one wife provided he treats them all with great kindness,love,equality and fairness. If he is unable to do so then plain and simple he cannot have another wife!Those who do contrary to this are certainly not on the path of the Prophet or his Sahabah who were always known to be the best of men to their wives.
Oh and if its the law of the land is to produce written proof of approval from the existing wife then the law MUST be abide by.
Finally the woman in the OP was sadly very foolish. One should never love another with this much passion that if he/her cheats you or betrays you that you then do something illegal and wrong to get back at them! It would have better for her to demand a divorce than killing the man and now warranting a jail term and possibly even death sentence not just for herself but her relative too!They just ruined themselves.. Tragic.