I don't want my mother-in-law to live with us after my wife gives birth
Do you not like your mother-in-law?
She has always treated me unfairly.
You should not have to live with your in-laws if she caused problems for you. It might help for her to be able to watch the kid sometimes to give your wife a break.
My wife just does whatever she wants.
You may want to have a discussion with your wife about this then, before it's too late.