Now 99, Mrs. Stoltz resided in an assisted living facility in the Bronx, where she had a one-bedroom — with meals and other services — for around $3,600 a month.

Ms. Sheridan, an interior designer (sheridaninteriorsinc.com), called her mother three times a day and visited once or twice a week, taking the subway from her combination home and office in Midtown.

But the services weren’t quite right for someone with Mrs. Stoltz’s condition, vascular dementia. She rarely went on the organized shopping trips and excursions. “You have to remember to get to the lobby and get on the bus,” Ms. Sheridan said. “That’s where my mother was really faltering.”

Mrs. Stoltz had additional help at bedtime, but hiring an aide for daytime hours was expensive and still not ideal. “The two of them would be staring into space,” Ms. Sheridan said. “My mother is not good at conversation these days.”

So Ms. Sheridan resolved to find a two-bedroom house for herself and her mother. They needed a yard, because Mrs. Stoltz likes to be outdoors.

They also required an entrance with few steps. With a top price of around $400,000, Ms. Sheridan went on the hunt a little over a year ago for a two-family, intending to have an income-producing tenant.

She focused on the Bronx, where housing prices were comparatively low, and where her mother’s doctors were.

But finding an easily accessible house and yard proved difficult. Most of the houses she saw were unsuitable in many ways. Ms. Sheridan assumed that two-family houses would be two side-by-side units, but what she came across was one unit atop another. The owner’s apartment was typically upstairs, sometimes with an exterior spiral staircase to the yard. Ground-floor apartments were usually small studios or one-bedrooms. Many places were in bad shape.

Last year Ms. Sheridan visited an upholstery shop she had heard about, Custom Design Studio, on Bruckner Boulevard in Mott Haven. The owners directed her to Allison Jaffe of Key Real Estate Services.

“I was concerned about what was available in their price range and about finding appropriate living space for them,” Ms. Jaffe said. A lot of sellers were “overreaching on their asking prices,” and reluctant to negotiate.

Last fall the women went to Throgs Neck to see a suitable place — a detached two-family Cape Cod, converted from a one-family. The listing price was $439,000. Ms. Sheridan offered $370,000, then $385,000. But, concerned about the lengthy bus-to-train or express-bus commute to Midtown, she declined to offer more.

A house-over-a-store situation arose at a mixed-use brick building on East Tremont Avenue in Schuylerville. A steep staircase led to the three-bedroom residential unit, but the owner had installed a stair lift in front. What they were seeking for Mrs. Stolz was access to the backyard, but as Ms. Jaffe reasoned, “If you can put a lift in the front, you can put a lift in the back.”

The asking price was $469,000. “I absolutely wanted it,” Ms. Sheridan said. She looked forward to updating the interior. As for the chair lift, “Mother enjoyed riding up and down in it.”

But she would need a commercial loan, which required a larger down payment and had a higher interest rate than a conventional mortgage. The purchase wasn’t financially feasible.

Another opportunity came in Allerton, where a semi-attached two-family house, in need of renovation, was listed for $449,000. The two-bedroom lower unit was larger than most and accessible through a door beneath the front stairs. Ms. Sheridan’s offer of around $400,000 was declined. The seller took the house off the market.

“He changed his mind and that was it,” Ms. Sheridan said.

After nearly a year, she decided to give up the hunt and leave her mother where she was. “I said O.K., I’m done,” she recalled. “I cannot go through this emotional-roller-coaster thing anymore.”

Late last winter, Ms. Jaffe contacted her about a place in Soundview, near Parkchester. This one was a bungalow, lacking a rental unit. Ms. Sheridan didn’t want to bother looking, but she went, getting lost on the way.

She was amazed to find almost everything she wanted. The house had three bedrooms, a fenced yard and even a dishwasher, something oddly hard to find.

“Judy was hesitant because this house was listed at $325,000 and there was no income potential,” Ms. Jaffe said. “But she walked in and said, ‘This is it.’ ”

Ms. Sheridan bought the place for $295,000. She and Mrs. Stoltz arrived in the summer. The early days were rough, while her mother got used to things.

Ms. Sheridan still works out of her Midtown home office a few days a week. Meanwhile, Mrs. Stoltz now has plenty to do. Even small chores, like emptying the dishwasher, “give her a sense of purpose and mission,” Ms. Sheridan said.

The neighborhood, largely Bangladeshi, feels like the suburbs, Ms. Sheridan said, with welcoming neighbors and “shopping malls instead of fruit vendors.”

She added railings to the stairs outside, “but my mother is doing so well here and is getting stronger, so the stairs are not an issue at all.

“There are days now when she doesn’t even take a nap, and that is so phenomenal for me. She is walking better, and she really helps me in the kitchen, and it’s a joyous thing to see.”

E-mail: thehunt@nytimes.com