If you have a month to month agreement with the landlady -- your wife's mother, then you might want to look for a place yourself, and quickly. I don't know the situation between you and your mother-in-law, but you can be ousted yourself within 30 days. Unless pursuant to some agreement, some type of rent control or stabilization or other law, she could give you thirty days notice that she is not renewing your lease. Depending upon the jurisdiction, you may get a maximum of 60 days.
I don't know the situation, but trying to oust your wife from the apartment owned by her mother seems a little unusal and unlikely. I don't know the situation but this may not be the best way to go about what you intend and perhaps you should consider seeking a new residence and fresh start. Additionally, while I'm sure you are aware and do have the best of intentions, your children are involved and any actions that could significantly hurt your current wife may also have effects upon your children -- who is their mother regardless of your relationship. Divorce is almost never a good situation and it is sometimes difficult to remember how the other players in this game can be affected, who are just as important if not more so.