A mother walks with her 1-year-old daughter in 2014 outside the shelter at the old D.C. General Hospital. The shelter has been at capacity for years, despite poor plumbing, heating and other problems. (Sarah L. Voisin/The Washington Post)

D.C. Mayor Muriel E. Bowser’s administration has cleared a major stumbling block in her effort to close the city’s dilapidated shelter for homeless families at the former D.C. General Hospital.

Attorneys for the city prevailed this week in zoning fights with neighbors of two of the proposed sites, winning approval to move forward with construction as early as November, although opponents could still file appeals.

The development gives the District a realistic chance to close D.C. General by 2020 — six years after the disappearance of an 8-year-old girl put a spotlight on city’s emerging epidemic of family homelessness and overcrowded conditions at the District’s main shelter.

The battles before the D.C. Board of Zoning Adjustment pitted Bowser and the D.C. Council against citizen groups that argued the government was trying to ram through construction without justifying zoning variances that would be required of private developers.

“We’re thrilled,” said Amber Harding, an attorney with the Washington Legal Clinic for the Homeless. “I think it came down to neighbors who had some concerns, and, rightfully, the needs of homeless families to have a place to live outweighed those concerns about parking and the height of the building.”

After winning office in 2014, Bowser (D) vowed to close D.C. General and replace it with smaller, safer shelters spread throughout the city.

The plan faced a backlash, however, that was amplified by revelations that some top donors to Bowser stood to gain financially from selling or leasing private land for the shelters.

The D.C. Council last year jettisoned sites connected to the mayor’s donors and selected others, but without public hearings or meetings with possible neighbors.

Two of the sites soon attracted opposition: One was slated for the parking lot of an upper Northwest police station, along Idaho Avenue, and another along Rhode Island Avenue in the 5th Ward’s Brentwood neighborhood.

At a marathon zoning board hearing last month, neighbors said the city never consulted with them about the sites and never considered what they believe are better alternatives for the shelters, each of which would house about 50 families.

But on Wednesday, the board approved the two sites, saying the benefits outweighed concerns.

“The traffic issue, I don’t think it’s going to be extremely burdensome,” board member Lesylleé M. White, said of the 3rd Ward site, adding that neighbors already contend with the police cars that will provide “24-hour security” for the shelter.

City officials seemed to have a plan to spread out families and not to put them “on top of one another . . . but have services so they could at some point move forward with their lives,” White said.

As the homeless problem grows in the District, however, it is clear that the network of new shelters won’t keep up with the need. The 250 families staying at D.C. General account for less than a quarter of all homeless families in city care. Several hundred have been placed in temporary shelter in motels, mostly along New York Avenue in Northeast.

David Brown, an attorney for two groups that opposed the sites, said he expects a written ruling within 60 days and then will consult with his clients about whether to appeal.

“Both of my clients feel that the city was given more latitude than the board would ever give to private developers — a long list of zoning violations were excused to make the projects work,” he said. “My clients feel like they have been victimized by a double standard.”