Jane Jetson is a stay at home mom in an era where that apologetic term didn’t exist (1962 when The Jetsons was produced, not 2062 when it’s set). She’s seemingly always available when her children and husband come home from school and work.
In an episode where she wants to drive, George is scared not only that she won’t be home when he gets there but that she’ll hurt herself on the road. She’s more clued in to the children than George though and generally brings George around to her and the children’s point of view.
She gets in a lot of shopping, suggesting that the Jetsons are not poor. She defers to George as implied head of the household but has a strong personal influence which she uses regularly on her behalf and the children’s. Failing that she has a “higher authority” she can turn to: her mother/George’s mother-in-law.