My mother has been living with my wife and our four young children for the last two years. I don’t have shalom-bais and I would like to know the halacha as it pertains to my mother living under the same roof with my wife and I. My father is deceased and has been since 1989.

You are not obliged to have your mother live with you in your house (of course if you're living in your mother's house or in a jointly owned apartment then that's a different story). In certain circumstances- if you inherited your father's estate and your mother did not ask to receive her ketubah from that estate- you are responsible to provide her adequate housing at your expense from the money you inherited. In other cases, she should pay for her own housing as long as she has the financial means to do so. If not, attending to that need is the first priority of your tzedaka. Kibud Eim- the commandment to honor your mother- requires you to act to your mother with deference and respect and to explain- in a way that minimizes the hurt to her feelings- why you are finding her alternate housing outside of your house.