The information from the excerpt which best supports the inference that nonstandard forms of English can express relationship nuances that standard English cannot is the following:
The author states that when she is around her mother or her husband, she speaks English in a nonstandard form. The way she talks to them, with mistakes here and there, shows the strong bond they have. It is the language the author grew up with, the one her mother has spoken for her entire life and has influenced the way she speaks, depending on who she is with. It is indeed a "mother tongue".