If you look for "the role of the wife in her family" or "the role of the woman in her family" in any good internet search engine, you will find numerous examples of both, and, since the person who wrote your text wrote these phrases in this way, it would not be incorrect for you to do the same.

See also:

Like the man, the woman plays a crucial role in God's pattern for the family. 2. Great damage has been done in many families because one or both of these roles ...
http://www.avondalechristians.com/index_files/3_roleofwoman_...
Factual discourse on the true role of a woman in the family and not the lies perpetuated by some men ...
http://www.youtube.com/watch?v=f7cfz5Wf-wk
Jul 2, 2013 - What is the role of a woman in a family and how has it changed? Has the role of a woman eclipsed those of a man? What is the significance in ...
http://prezi.com/xddymv5ya20b/women-play-a-more-important-ro...
Feb 11, 2012 - The role of the christian woman in the family. After God created man, and gave him dominion over every living thing, Man was not satisfied .
http://talkingforjesus.blogspot.gr/2012/02/role-of-christian...