The children grow closer with the mother than the father, merely due to the extreme amount of time being spent with the mother in comparison with the father. This leads to competition between parents for the children's affection, as the father looks for ways to make up for the time-gap, perhaps through many gifts/monetary offerings, perhaps by being more lenient/a pushover. Meanwhile, the mother often feels the need to prove her closeness to the children, since a) that is the purpose for which she gave up her career b) this is proof of her ability to be a good homemaker, and is her major source of self-validation in a career's absence c) she is sensitive about her inability to provide the children with monetary support, and must compensate with emotional support. Proving she provides this support is proving that she contributes a lot to her family despite not contributing at all financially.
At the same time, mothers may grow either resentful of their children for being the obstacles to their careers, or overly attached to their children, since they are the major source of meaning in the lives of their mother's now that career, which can be a major source of meaning and self-fulfillment, has been taken away.
This scenario is not true of all families with stay-at-home moms, many of which are happy families. But the stay-at-home mom scenario has many potential ways to lead to a very unhealthy family dynamic, and is far from the ideal that anti-feminists would have us believe.
I advocate family values; I believe a family is happiest when each parent is allowed to pursue a path to self-fulfillment that enables them to be a better parents. Some mothers and fathers may find that path to be through being a stay-at-home or part-time working parent, while some may find it by having a full-time career. But when society encourages flexibility in terms of how the work - providing for the family's financial needs, parenting-work, and household chores - it is the family who benefits. Happy parents are better parents.
