I just recently read The Left Hand of Darkness, By Ursula K. Le Guin. I think that if it does not contains the answers you seek, at least it shall be a great source of inspiration.
The story happens in a world where the people are all hermaphrodites. They remain assexual for all purposes for 22-24 days, then go into oestrus for 2-4 days. During oestrus their bodies will develop either male or female secondary characteristics, depending on environmental circumstances and chance. For example, for those who go into oestrus alone they have equal chances of developing male or female characteristics, but if they go into oestrus around other people who are also in oestrus, their bodies will react to keep the numbers of male and female individuals approximately equal.
If they get pregnant, they will keep the female characteristics until a few months after childbirth.
Last but not least, they have no concept of marriage as we know it. They may vow fidelity, but it only means "I will always have intercourse with you whenever our ouestrus is in sync and you are around", not "I will be faithful until death do us part".
Due to this, any person can be a mother to a number of children from many fathers, and also a father to another amount of children from many mothers. They keep a loose track of who is father to whom, but mother-to-child bonds are nearly sacred. Thus clans are "matriarchal". But since everybody has both sexes, the term "matriarchy" is probably not the most appropriate one. The people from the book live in a society where the very concept of gender does not exist outside the physical part of sexual intercourse.
Therefore, every clan centers on a parent individual that has nursed their children.
There is a short story by the end of the book about a clan that takes pride on their children always having their first sexual relationships as females, and pride on not taking vows of fidelity. But this is the same kind of pride that a family from Earth could have about, say, having many engineers or doctors in the family, or making nice pies.
Seriously, go read that book. It's an awesome read. Praise the creation unfinished!