Sentence:  A husband will thus have responsibilities to his own household, as well as to those in which his “<WSD>outside</WSD>” children reside. 
Meaning of the word marked with <WSD> tags:  Not legally married to or related to (e.g. not born in wedlock to), and/or not residing with, a specified other person (parent, child, or partner);  existing between two such people. (out of wedlock), (nonresidential).