It takes time to build a relationship and win the trust and confidence of those who are already there. It applies in the field of work as well as at home.
Start by taking charge of few activities and win their heart by pouring love and care. Avoid confrontations as they only make things worse.
With passage of time your mother in law will realize that you are there to add value and not take away anything. With passage of time a friendliness develops and with that comes mutual care, trust and confidence. Once that happens, your mother-in-law will be more than willing to let you take more and more responsibility and eventually hand over the charge of her son and the household to you.
Affectionately,
Alok da.