Editor's note: Kelly Wallace is CNN's digital correspondent and editor-at-large covering family, career and life. She is a mom of two. Read her other columns and follow her reports at CNN Parents and on Twitter.
(CNN) -- Samantha Sleeper, a fashion designer and co-founder of a tech company, didn't set out to be the primary breadwinner for her family.
"It was definitely not a conversation where we sat down and said, 'OK, I am going to go to work, and you're going to be more at home,' " said the Brooklyn, New York, mom of a nearly-1-year-old son. Her husband is a professional musician.
"We both worked, and then, by opportunity, I became the one who was working for more of the income," said Sleeper, who runs her own business designing women's apparel and helps lead Purely Fashion, an app connecting consumers with designers.
"I think there are mixed emotions about it," she added.
In four out of 10 households with children, women are the sole or primary breadwinners, according to a 2013 report by the Pew Research Center. Now, based on a new survey, we have an idea of how many of these breadwinning moms are feeling about their roles.
The 'pleased' vs. 'reluctant' breadwinning mom
The national survey by Working Mother Media found that breadwinning moms who have partners and who didn't choose to be the primary earners in their families tend to feel less satisfied about their lives than women who consciously selected the role.
In the survey of 2,000 working moms and dads, including 820 breadwinners who have a partner, only 29% of the moms said they became breadwinners by choice, versus 71% who fell into the role by circumstance, chance or luck (59% of breadwinning dads said they chose the role).
When asked how satisfied they were on a host of questions related to family life, there were significant gaps between breadwinning moms who said they were pleased to be the breadwinner and those who said they would prefer that their partner outearn them.
The survey found that 89% of the moms who were happy to be breadwinners were satisfied with how much their spouse or partner took care of the children, versus 58% for the "reluctant" breadwinners. Meanwhile, 75% of "pleased" breadwinning moms were satisfied with how chores were divided at home, versus 48% of the group who would prefer not to be the primary earner.
Fighting the impulse to rearrange the dishwasher
Gina Rau, a mom of two in Portland, Oregon, puts herself in the "pleased" category. When she and her husband got married and talked about having children, the decision that she pursue a career and he be a stay-at-home dad was "something we both naturally agreed to."
"For us, it's divided up as if both household manager and full-time career person are equal, so my husband takes care of most of the household and other responsibilities while I still participate but not to the degree that he does," said Rau, who runs her own business doing marketing and brand consulting for startups and larger companies.
That means learning how to let go, she added.
"You know, just like at work, I have to release responsibility to co-workers who are taking on a project, I have to release responsibility to my husband," said Rau. "If he's going to load the dishwasher a certain way, I have to not rearrange it because I would do it differently."
The survey also found big differences between breadwinning moms and dads overall when to comes to satisfaction with family life. No surprise, breadwinning dads report greater happiness: Seventy-six percent of men were happy with the division of household responsibilities, versus 60% of women, and 85% of men were happy with how the child care is being handled, versus 71% of women.
"Stuck in ... traditional roles at home"
Catherine Martines Mortensen, a public relations specialist who became the primary breadwinner after a family-run small business struggled, said she still does most of the household chores.
Martines Mortensen sometimes wishes her husband would pitch in more, but she also struggles with that role reversal, said the mom of two from Fairfax, Virgnia, whose kids are 16 and 10.
"Even though I enjoy being out in the workplace and I enjoy bringing in a paycheck, part of me still feels like ... I want to be that old-fashioned mom," she added.
Samantha Ettus, a work/life management coach, said that in many ways, women and men are "still stuck in sort of traditional roles ... even if they have big roles at the office."
Sleeper, the fashion designer and tech executive, said it's hard to change that mindset. "So, no matter how progressive I think I am, at the end of the day, if I come home and my house is still a disaster, I feel a sense of inadequacy," she said.
"Women tend not to have high enough expectations that their spouses will be partners, and so they accept treatment and roles at home that they might never expect at the office," said Ettus, who is working on a book about how working moms can have the best lifestyle possible.
"Let Dad be the dad he wants to be"
Carol Evans, president of Working Mother Media, who has been a primary breadwinner since her first child was born 27 years ago, said the survey shows that moms who outearn their husbands and who feel the primary responsibility for the house and the kids should learn to let go -- even a little bit.
"I'm always saying to (moms), 'let Dad be the dad he wants to be. Let him build his own relationship. Make him responsible for his relationship to the kids and to the house,' " said Evans, whose kids are 24 and 27.
One thing both breadwinning moms and dads agree on, according to the survey, is how expectations about family roles still need to change, with 74% of breadwinning moms and 72% of dads saying society remains more comfortable with men as the primary earners even after the recession.
"You still see commercials where it's the woman cleaning the floor, not the man cleaning the floor, like in my house. You don't see that," said Rebecca Hughes Parker, a mom of three who is her family's primary breadwinner and who admits to barely knowing how to use the washer and dryer.
With the number of breadwinning moms expected to grow, society's portrait of the typical family is likely to shift. The impact on our children, however, is already apparent.
When Hughes Parker, who writes about being a breadwinning mom on her blog, and her family were picking pumpkins at a farm during the fall, they saw a hen with chicks. After they pointed out the chicks to their youngest daughter, who's 3, she looked at the hen and said, "What's that, their daddy?"