Mostly an anime trope: one good way to show how sweet and caring a mother is, is to depict her with her hair tied in a loose plait and put on her shoulder. For some reason, this detail immediately tells the audience "hey, this mom has to be a nice and gentle person!".
This can be explained by the fact moms have less time to spend on their appearance. Since the makers of a show probably don't want to make their characters ugly, one way to demonstrate mom-hood is to give her a low-maintenance hairstyle. Housewives (most likely to be the mothers of young children) also need a hairstyle that's going to stay out of the way when they're doing housework and cleaning up. May or may not come with an apron to further emphasize.
A subtrope of Long Hair Is Feminine
, and more generally Expository Hairstyle
Contrast Braids of Action
, Tomboyish Ponytail
and Tomboyish Sidetails
Anime and Manga