All sorts of things can go wrong while you’re managing the sandwich counter at a busy grocery store. Just ask Mairead Hill, who has charmed her way through many a mishap while running the Woodacre Country Market & Deli for the last decade. 

Over the years, Ms. Hill has learned that virtually any obstacle can be overcome with the help of a loyal staff and a devoted clientele. One day, when she sliced the tip of her finger while cutting a sandwich, a customer repaired her digit with Krazy Glue, sparing her a trip to the E.R. Another day, after the diamond on her engagement ring disappeared, a customer gave her a new one.

The first was a firefighter, one of many employed at the station around the corner. The second was a professional jeweler—and a very generous man. 

“My customers are everything,” Ms. Hill said. “They make my world go round. I can come in with dirty hair and a tired face and they will tell me that they love me and I’m beautiful.”

Before taking over the store, which she co-owns with her father, Hanna Anki, Ms. Hill was an elementary school teacher at the Saint Raphael School in San Rafael. Making sandwiches was not part of her career plan.

She was passionate about education until she found herself coming home in tears one too many nights. She enjoyed putting together lesson plans and interacting with kids, but imposing classroom discipline didn’t come naturally. Nor did coping with fussy parents.

An alternate path awaited, and she decided to follow it straight into the family business. Her parents owned and operated the Lagunitas Store for many years, and her father and uncle had more recently purchased its Woodacre counterpart. They needed someone to help run it.

Ms. Hill took on evenings and weekends at the store while continuing to teach. But when she gave birth to the first of three sons 11 years ago, holding down two jobs became untenable.

For her, it seemed an obvious choice: She couldn’t bring her baby to school, but she could bring him to the store. So off to the deli he went. She carried A.J. in a sling while serving customers.

“I didn’t want to leave him,” said Ms. Hill, who is 43. “I brought him to work right away. I never even took time off, really, so he always came with me. It just made sense.”

She trained A.J. to nap during the lunch rush, putting him down in a crib in a darkened storage room. It all worked swimmingly until a county health inspector showed up and told her to get rid of the crib. “Technically, you can’t have a living space inside a business,” Ms. Hill said. “I think she could have overlooked that, but she said I needed to remove it. When she left that day, I bawled my eyes out.”

Even after she hired a babysitter, all three of her boys—A.J., Finn and Michael—still spent plenty of time in the store. If they got fussy, her staff would rock them to sleep while she worked the counter.

Her teammates, whom she considers family, have been with her for a decade or more. Efrain Martinez, the chef, runs the kitchen; Mauricio Loaiza opens the doors six days a week and does a little of everything; and Rosa Manzo helps behind the counter. “I could never do this without them,” Ms. Hill said. “They are incredibly loyal and trustworthy, and they would do anything for me.”

A rotating cast of middle-school interns help out at the register, and some graduate to formal jobs.

As a boss, Ms. Hill isn’t much for hierarchies. When it’s time to sweep, she’s as likely to grab the broom herself as she is to hand it to someone else—a practice she inherited from her mother, who managed the Lagunitas Store for 30 years.

“I never felt like I was the boss, and I don’t think Mairead does either, you know,” said Maire Anki, a native of Northern Ireland whose voice maintains its charming lilt. “She just thinks everybody’s on the team and equal to her, if you know what I mean.”

The diversity of the team is an essential part of what makes the place appealing to customers like Jacobo Benito, who has been coming to the deli since arriving in the United States from Mexico at age 2.

“The owners are people persons,” said Mr. Benito, 25. “They are always welcoming and inclusive. These guys know their clients, they know their markets and people. They will do their best to try to keep everyone happy in all possible ways.”

The menu features an array of 28 deli sandwiches as well as soups and daily specials, but it’s the breakfast sandwich that keeps Mr. Benito returning. As a kid, he’d have one on an English muffin with a bottle of apple juice to wash it down, but lately, he’s been switching it up. “After many years, I’m now doing a breakfast croissant,” Mr. Benito said.

In addition to her deli family, Ms. Hill’s blood relatives are fixtures at the store. Her sister, Shirene, does regular shifts on Fridays, and her parents contribute in crucial ways. “This job entails a lot of schlepping behind the scenes, and they help me get things when we run out,” Ms. Hill said.

Her mom has a knack for stocking items that people don’t want to go over the hill to purchase, such as spray starch or sunflower oil. Her dad helps select the wines—they have a pretty extensive selection—and he keeps the books. The latter task includes maintaining a box of file cards to keep track of how much customers on credit owe at the end of the month. “Some people have to wait until they get paid or receive a Social Security check,” Mr. Anki said. “They’re almost always good for it.”

Like his daughter, Mr. Anki, a Palestinian who grew up in Jordan, prefers bold fashion statements. On a recent Friday, he dropped by in a blue-and-yellow Golden State Warriors blazer, which he rotates with his San Francisco 49ers and Giants jackets. Mairead wore a fluorescent green tank top, DayGlo dangle earrings and a pair of funky green Jayli coveralls. 

“I’m a sparkle person,” she said, stressing her affinity for glitter. “I’m a kid for life.”

Her affable father, who is 73, wears his thinning, wavy salt-and-pepper hair in a short ponytail; she wears her blond locks long and straight. There’s no mistaking whose genes she inherited, and her mom gave her a Gaelic name to prove it. Mairead—it rhymes with “parade”—ties up a lot of tongues, and Ms. Hill sometimes wishes her mom had given her an easier name to pronounce.

Her dad came to the United States at age 19 with $300 in his pocket. Maire met him on a post-college summer vacation, when a friend took her to a San Francisco restaurant where he was waiting tables. It was her first night in the country.

“I hadn’t really been out of Ireland much before,” Ms. Anki said. “I guess I just liked the dark, curly hair, and he just liked the blond.”

They both grew up amid violence and war—and in cultures that placed a premium on family and food. The deli menu features a corned beef sandwich, of course, and a rotation of Middle Eastern specials, most recently a Lebanese fattoush salad.

Ms. Hill embraces both sides of her identity with equal enthusiasm. “I love that I’m first-generation,” she said. “I’m really proud of it.”

The store is open from 8 a.m. to 7:30 p.m. daily.