AGONY: My wife has denied me sex because of my sister

RELATIONSHIPS & DATING

I have been married for four years, with two sons. When I met my wife, I was living with my sister and mother. Now, she wants my sister to leave. I am uncomfortable throwing her out. 

I have explained to her that we don't have to make it look like we are chasing her, but we could use other means to get her out of our house so that we remain in talking terms.

I have asked my sister to stay in the boys' quarters, as she plans her next move, but my wife is too impatient. I don't want my mother to know our struggles because she will be hurt and will resent me and my wife. 

My wife does not care, but I do care because I don't want a wife that is resented by my family, especially since I am the firstborn.

How do I explain to my wife that my reluctance to act is for the good and harmony of the family?

We have not been talking for nearly a month and she has denied me sex for about three months.

James, Bulenga