Mothers, but not fathers, with multiple children report more fragmented sleep. Mothers with multiple children report more fragmented sleep than mothers of a single child, but the number of children in a family doesn't seem to affect the quality of sleep for fathers, according to a new study. Source 1k.
I would say it depends. But on the whole, I would say yes. Typically, mothers tend to worry more than fathers. And I would expect it happens up through adulthood. So I would say that would contribute to a lack of sleep.
It makes sense. Mothers are expected to do a lot of things, not only provide income, but to be up to date in their children's lives with social outings and other things of that nature.