Virginia Gov. Charles S. Robb today selected a 46-year-old Annandale woman to a top business regulatory post, capping a three-month, behind-the-scenes lobbying battle between warring labor and industry groups over the appointment.

The naming of former U.S. Treasurer Azie Taylor Morton, a business consultant and Democratic Party fund-raiser in Fairfax County, to be the state's commissioner of labor and industry was viewed as a compromise move. Robb's earlier choice for the slot, former Labor Department official Robert Lagather, had been strongly opposed by a number of politically powerful business groups, including the Virginia Manufacturers Association and the Virginia Coal Association.

With the appointment of Morton--coupled with the naming yesterday of Harry Dean Childress, a Clinchfield Coal Co. assistant superintendent, to head the state Division of Mines--Robb apparently managed to extricate himself from a political bind that has been plaguing him since he took office Jan. 16.

The United Mine Workers, the only union that actively supported Robb's campaign last year, had waged an all-out campaign for the ouster of incumbent Mine Division director, McLynn Sharpe, a former Westmoreland Coal Co. executive. UMW president Sam Church had visited Robb to complain about Sharpe, whom the union has blamed for Virginia's record on mine fatalities, considered among the worst in the country.

Sharpe had been strongly supported by the Virginia Coal Association and many mine owners, who pumped about $300,000 into Robb's campaign, more than any other special interest group.

At one point, Robb sought to pacify both sides by offering to reappoint Sharpe, but naming Lagather to the labor and industry post. Both sides rejected that proposal.

After Robb aides notified coal operators that Sharpe would not be renamed, they heavily supported Childress, whose resume was first dropped off with the the governor's office last week by Blaine Carter, the coal association lobbyist. Clinchfield Coal, Childress' employer, contributed $32,000 to the Robb campaign last year.

In addition, Childress was strongly supported by Jim O'Quinn, a shy, retiring car dealer from southwest Virginia who gave $25,000 in cash and more than $8,000 of in-kind services to the Robb campaign last year.

O'Quinn, the largest single contributor during last year's campaign, said today he knows Childress from their joint service on the Dickenson County School Board.

As head of the labor and industry department, Morton, who used to work for the Texas AFL-CIO, will oversee a wide-ranging business regulatory apparatus that includes the state's embattled occupational safety and health program as well as the mine division. Her appointment today was hailed by labor. "The governor has done the working men and women of this state a great service," said state AFL-CIO secretary-treasurer David Laws.

Business groups, meanwhile, professed to have no knowledge of Morton, but said they were pleased that Lagather didn't get the job as well as the appointment of the 30-year-old Childress. "On balance, industry came out fine," said lobbyist Carter.