A short article on Roman family life is at an Internet site called "The Roman Family" at http://ancienthistory.about.com/homework/ancienthistory/library/weekly/aa081997.htm?terms=family.
There is much more at http://ancienthistory.about.com/homework/ancienthistory/sitesearch.htm?terms=family&SUName=ancienthistory&TopNode=4911 which is the first page of a list of 173 links having to do with various aspects of life in ancient Rome.
Daily life, Family, and Women are covered in lists of web sites at http://members.aol.com/Tchrfromoz/romans.html#daily life , and at http://www.fordham.edu/halsall/women/womensbook.html#Rome, you can find scads of information on the position of women in the Roman world. (Scan up or down for the same type of information in other places and times.)
Finally, if you want to really know about the specific legal rights of persons as members of families or society, go to http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman/Texts/secondary/SMIGRA*/Law/home*.html#persons. The same page has lots of other info on rights and duties in a system which was much more legally defined than our own.
Descriptions of how Romans lived have to be taken with a huge grain of salt. It is important to remember the size of "ancient Rome" and how long it lasted -- even by the most conservative estimates, more than a thousand years. There were millions of citizens just in Italy and many millions more in the full extent of the empire. In most places, family life was a product of pre-existing customs and practices.
Most of the Internet and book resources that deal with life in "ancient Rome" really deal only with the lives of rather prosperous urban citizens of Rome itself and their families, and usually in the fully developed but not yet crumbling Empire phase. The lives of "freedmen" -- former slaves, who were either gifted with their freedom by their masters of who purchased their own freedom -- mirrored, although usually on a smaller scale, those of citizens. In later stages of the Empire, freedmen had all the rights of citizenship and lived just like freeborn citizens of equal means. Slaves, who were the majority of the population, and women, of course, didn't count, and their status and lifestyles were determined completely by those on whom they were dependent.