"But don't forget that as long as God gives you life we will still be mothers and no matter how revolutionary you may be, we have the right to pull down your pants and give you a whipping at the first sign of disrespect."
Not all Matriarchs are malicious, and not all Mama Bears are young. These grand dames are the grandmothers, aunts, and headmistresses who care for their children, students, or even employees with an iron discipline the army would envy. The Apron Matron has a larger than life, imposing presence and leads with a personality more forceful than a wrecking ball.
If there's combat to be had, she can take on a brigade on her own, even chasing out ninjas armed with naught but a broom. (Sadly, she'll often be captured and bound).
Expect her to be motherly, caring, strict, and kind. Also, probably "plump" yet strong. If married, she's likely to have a Henpecked Husband, though she's usually single either from outliving her husband or never marrying.
Can overlap with Mama Bear, and must be written carefully to avoid Flanderization into My Beloved Smother. Compare The Patriarch, whom she may be married to. See also the Mammy.
If an Apron Matron has enough prestige, she will likely become a Grande Dame.
Miyabi Kagurazaka from Ai Yori Aoshi is a somewhat younger version.
Martha from Yu-Gi-Oh! 5Ds. She's such an overbearing Mama Bear that the two main characters, Yusei Fudo and Jack Atlas, are reduced to trouble-making ten year olds in her presence. And only she's got the guts to pinch Yusei by the ear.
A character in Pokémon: Lenora, the Nacrene City Gym Leader, seems to be borderline this, though she isn't shown to have children (she is in charge of the museum, though). The apron, though, only appears on her in the Japanese verison of the anime and her video game sprite, as the animators feared US viewers would see her as a 'mammy' stereotype, since she's of African descent.
Ma Joad. Even the characters acknowledge she's the one that holds the "fambly" together.
In Suite Française, Charlotte Péricand. She runs her household with great efficiency, and when fleeing from enemy bombing she acts to save her children with ruthless decisiveness (as long as the family's alive, nothing else matters). However, she usually fails to match the "caring" and "kind" part of the trope description by her lack of real empathy, even though she conscientiously tries to carry out the duty of being good-hearted and generous.
Amelia Peabody Emerson. Her parasol is a weapon feared throughout Egypt (before her husband gave her a sword-cane version), and senior British officials cringe at the thought of her tongue-lashings.
"The Gordon Women", in the Mc Auslan short story collection by George Mac Donald Fraser, is dedicated to this trope (along with a mixture of the Proper Lady and Iron Lady tropes). The star of the show is his Aunt Alison, who manages to defuse a potential crisis through acting and sheer steel nerves, much to her nephew's amazement.
Here was this good, respected widow lady of advancing years, who had guided my infant steps, heard my prayers at night, and read to me from the Billy and Bunny Book, sitting there looking like the matriarch of some soap-opera family of Texas tycoons, and apparently concealing the combined talents of the Scarlet Pimpernel and a Mafia godmother. I didn’t know where to begin.
In A Brothers Price, the first daughter to be born to a group of sisters is given the title/name Eldest. When she and her sisters marry and have daughters of their own, she becomes known as Mother Eldest, and she's the head of the family. The family's husband, if they're lucky enough to have one, takes on the softer and more nurturing aspects of childrearing, helped somewhat by Eldest's younger siblings. Eldest's role is more disciplinary, but in the case of the Whistlers at least, not without affection.