Apron Matron

"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."

—Úrsula, One Hundred Years of Solitude

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.

Examples of Apron Matron include:

Anime

Dola the Sky Pirate captain from Laputa: Castle in the Sky. Very plump, very matronly, very very iron-willed.
Chizuru Naba in Mahou Sensei Negima is basically an Apron Matron in self-training. Given that she's only 14/15 now, she'll have the part nailed by the next twenty or thirty years.
- And from the Magic World, we have Mama, who takes the Mama Bear trope literally, being a giant teddy bear of a woman who will beat up anyone who abuses the slave girls under her care.
Sis from Now and Then, Here and There.
Helga from Dinosaur King is one who works for the bad guys, she's their housekeeper. She's superhumanly strong and resilient... because she's a robot.
Izumi Curtis from Fullmetal Alchemist will proudly proclaim herself a housewife while simultaneously kicking the ass of every single person/chimera/immortal who dares to hurt her surrogate kids.
- Then she beats said surrogate kids up herself! And when your surrogate kids are two of the most brilliant combat alchemists in the world, that's saying something.
Ishizaki's mother in Captain Tsubasa.
Miyabi Kagurazaka from Ai Yori Aoshi is a somewhat younger version.
Martha from Yu-Gi-Oh! 5D's. 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.
Pokémon Leona, the Nacrene City gym leader, seems to 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.

Comic Books

Granny Goodness. A real doting sort, this one. A villainous version of this trope. Voiced by Ed Asner (in an homage to old Boris Karloff movies) in the DCAU, Granny is quite literally child abuse incarnate. Her specialty is warping the minds of chidren with torture and brainwashing to become Tyke Bombs, while saying and genuinely believing that she's actually being kind to them by doing so.
Abigail "Ma" "the Red Tornado" Hunkel in the Justice Society of America, which back in the 40s was combined with Sweet Polly Oliver.
Monstress from the Postboot Legion of Super-Heroes. She wasn't any older than the others, but she was a lot bigger, and had a motherly attitude towards her teammates, often calling them "dear."
Thorn's grandmother, Gran'ma Ben, from Bone. Of course, she is a Queen.
Maw Broon, from the Sunday Post comic strip The Broons, is probably the example that every Scot will recognise immediately. She has eight kids and her own published cookbook.

Film

Ma Bell in I'm Gonna Git You Sucka, who is also a Mama Bear. On two occasions she singlehandedly takes on several evil henchman at once.
Martha Mc Candle in Big Jake .
Julia Moore in We Were Soldiers. She was a magnificient Team Mom to all the other Girls Back Home during the battle.

Literature

The archetype of The Virtuous Woman in Proverbs
As quoted above, Ursula Iguaran-Buendia from One Hundred Years of Solitude. At least until she was confined to her bed due to old age.
Marya Akhrosimova in War and Peace. She's the sort who speaks her mind, and to hell with aristocratic pleasantries.
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.
Rachel of Memory, Sorrow, and Thorn. Her strictness earns her the nickname "the Dragon".
Molly Weasley from Harry Potter, stern, happy homemaker or Ass kicking witch? How about both?
- Augusta Longbottom also qualifies, although she's less kindly and there's no way anyone could capture her.
- Minerva McGonagall also exemplifies this trope. Combines nicely with Stern Teacher.
The Badger Mothers in Redwall generally fit this, with Bella of Brockhall probably the most so.
Gytha "Nanny" Ogg from the Discworld novels. Her daughters-in-law might have a wholly different view of her, though.
- Lady Sybil, also from Discworld, who has had several Crowning Moments of Awesome in recent appearances, and was pretty formidable to start with—all you need to know about her is that she's happily married to Sam frigging Vimes.
  - It runs in the family. Her Great Aunt once sent a bandit who tried to rob her coach crying for his mother.
Mother Superior Mary Francis in James Byron Huggins' novel Cain. Frail, aged nun vs. demon-possessed assassin/cyborg/vampire?

Cain: "Holy water, Mother?"
MSMF: "No. Gasoline."

- Somewhat later, she goes out with a literal bang, taking out an army of minions with a bandolier of grenades. (No, she's not the protagonist.)
Razo and Rin's mother in Shannon Hale's Bayern series, the matriarch of a large and unruly family. Five of her seven children are bigger than she is, but guess who's unquestionably in charge?
Mama Thames in Rivers of London, do not get on her bad side.
Sarah Heap becomes this in Darke, keeping the peace between Septimus and Simon in the Heap home and keeping the place in order.
The ideal Barrayaran woman in Vorkosigan Saga was this. Cordelia played along but did not necessarily just Stay in the Kitchen.

Live Action TV

Nora Walker in Brothers and Sisters.
Marie from Everybody Loves Raymond.
Madea from the Tyler Perry plays/films/television shows etc.
Jeeves and Wooster: Bertie Wooster's Aunt Dahlia. His Aunt Agatha, on the other hand, is more of an Evil Matriarch.
Last of the Summer Wine is just crawling with 'em, although Nora Batty is probably the chief harridan among them. Many of them had a Henpecked Husband earlier in the series but are by now widowed.
- Glenda was introduced as a contrast. A mid-30s newlywed with different attitudes. After more than twenty years in the show she was clearly being assimilated by the others.
On No Reservations, they are a frequent and reliable source of a good meal in Bourdain's travels.
Michael Westen's mother in Burn Notice. Even Michael is slightly afraid of her.
Mam Boswell of Bread
Thelma Harper in skits on The Carol Burnett Show and the sitcom Mama's Family.
Many of the "Pepperpots" in Monty Python's Flying Circus
T'Pau, a ferocious old Vulcan tribal elder in Star Trek: The Original Series' "Amok Time".
Ruth from Six Feet Under.

Video Games

Plum Kitaki from Apollo Justice: Ace Attorney fits most of the details in the original post to a T. Especially the bit about being armed with a broom that is, in fact, a katana.
Mitsuko the Boar of Bloody Roar.

Web Comics

Despite having appeared in a grand total of three strips, Fanon has ascribed these traits to Doris in Misfile. She's also something of a Memetic Badass too.
Aunt Nina of Lackadaisy Cats.

Western Animation

Mrs. Slaghoople, Wilma Flintstone's mother.
A waitress who helps the gang out in the Ben 10 episode "Ben 4 Good Buddy".
"Sugah Mama" from The Proud Family.
John Stewart's landlady in an episode of Justice League, who attacks The Flash with her broom after mistaking him for a supervillain when he comes looking for the missing GL.