The thing is that quite posibly that married women are less happy (average) has to do with other factors present in traditional relationships, not with being married or having children. Related and common to married women, but not because they are married.

But it is a fact that when having a child, the first months it is difficult to sleep. Having paid maternity leave helps. Having extra help at home helps. Not having to worry about bills helps. You name it.

Identifying those things might help to imrpove happiness for married women with children. Full disclosure, I'm not single, but I have been and was happy. I'm still happy but one of the things that make me remain happy as opposed to other relationships is the fact that we agree on paying someone to do the domestic chores that none of us likes. Reduces fights and get us more free time to spend on things that we like to do so we enjoy mutual company.

My take is that for married women to be happier, they need to reach agreements with their husbands were the day to day stuff that causes stress, fuights and unhappiness is reduced. Sometimes with traditional marriages that doesn't happen because "it is assumed that it is women's work". And that asumption causes frustration and unhappiness.

Averages don't show the causes, just point out that there is something that doesn't quite work.

So in most cases it is not the children or the husband, but other things like feeling underapreciated or overworked. Or sometimes because they have to give up dreams/projects that they could have done if they remained single. In that situations, compromise, help and appreciation might help to increase happiness.

To put an example, now that my mother is retired she is way more happy than when she worked because she can do what she wants. Also distribution of house chores is more equal with my father, so that alsp helps. When we were little, she worked and did most of the caring/house chores. She didn't had much time for herself and that make her less happy.

It is not about demonizing people, it is about improving relationships. But the fisrt step is identifying the problem (that might be on how companies expect people to work more than 40 hours/week) and doesn't leave time for people to have a life outside work.