The petition, filed by members of rival organization National Union of Healthcare Workers, would bring about an election for members of Service Employees International Union-United Healthcare Workers West.
In San Francisco on Tuesday, about a dozen members spoke to television cameras at the NUHW union hall on Golden Gate Avenue.
"They left us with no voice at all," said Angela Glasper, who is employed with Kaiser in Antioch and has worked for the health care giant for 23 years. "Today, we are taking back our union."
The struggle between the dueling unions dates back to at least January 2009, when SEIU officials from Washington, D.C., took over Kaiser workers' local union, ousting thousands of health care workers from elected positions.
SEIU-UHW spokeswoman Adriana Surfas said the former union leadership was removed from office for "undermining union democracy" and misusing members' dues. She said they have since been found by a federal judge and the National Labor Relations Board's general counsel to have "deliberately harmed SEIU-UHW members."
Immediately after the shakeup, the ousted leaders formed their own union, NUHW, and have argued that SEIU-UHW has failed to represent Kaiser employees in the workplace.
Other speakers at Tuesday's press event said there is a "tremendous amount of intimidation and violence" occurring in the workplace and beyond, and hope that their decision to split from SEIU will re-empower unions across the state and country.
"This is going to define the labor movement in this country for many years to come," Kaiser San Francisco worker and NUHW member George Wong said.
Not since the United Auto Workers organized Ford in 1941 has the labor board scheduled an election for so many private-sector workers.
SEIU members said they are concerned the vote could put at risk the hard-fought gains represented by the recent agreement, which provides 9 percent raises over three years - or 3 percent each year - and protects all benefits through 2013.
"It sickens me that after we spent the last four months fighting ... NUHW would swoop in and try to take it all away," Maria Rangel, a unit assistant at Kaiser in Antioch, said in a UHW statement.
But members of NUHW said there has been a cultural shift in their workplace since changes were made to the union.
"We want a union that is honest with us and gives us a voice, one where our leaders are held accountable," said David Shapiro, a medical social worker at Kaiser Sacramento who was removed from his leadership position with that union, one of 32 unions that represent all Kaiser workers across the state.
Since the SEIU trustees took charge of the union, at least 1,500 positions have been eliminated, NUHW vice president John Borsos said. Others, such as about 400 pharmacy technician jobs, have been converted to "flex" positions, meaning workers no longer have a set schedule at a single location.
Surfas said, however, that no union members lost their jobs as a result of the position eliminations. "Nearly every affected union member has found a permanent position," she said.
"It's hard to deliver quality services in an environment like that," Borsos said. He said he believes what happened with the pharmacy positions is telling of what's to come for the thousands of other positions throughout the state.
Representatives from SEIU standing outside the NUHW meeting hall said they are more satisfied with the state of their union now.
"Our business was being mishandled," lab assistant and SEIU member Lisa Cox said. "We want fairness, and we're more member-driven now."
SEIU-UHW is the largest hospital and health care union in the western U.S. with more than 150,000 members, and is part of the 2.2 million-member Service Employees International Union.