Ms. Perry and Ms. Calcaterra were seated near one another. The two were barely on speaking terms.

Ms. Perry was asked to give an update on investigations. Prompted by one of the co-chairs, she began to detail some of the obstacles she and her investigators faced, attendees said: The governor’s office was editing letters, telling her what subpoenas she could not issue and dictating what investigative avenues she could not pursue. Her voice cracked with emotion.

And Ms. Calcaterra typed away furiously on her BlackBerry.

That same day, Mr. Cuomo publicly affirmed that even his own political dealings would be fair game for the commission investigators. “They have total ability to look at whatever they want to look at,” he told reporters during a stop upstate.

Yet at least four commissioners — including the district attorneys from Broome, Erie and Rockland Counties — began discussing quitting the panel to protest the interference from Mr. Cuomo’s office, commissioners said.

“There were some people that expressed the view that, ‘Look, it’s the governor, he created us, he gets to say what he wants,’ ” one commissioner said. “That was not my understanding going in. And it was not what he said at the press conference, and it was not what most of us wanted to do — participating in a commission that was not independent.”

Ms. Rice proposed asking the governor’s office to replace Ms. Calcaterra, according to emails and interviews. Others wanted to seek control over the commission’s budget and personnel, or halt communications between the governor’s office and commission staff. Several wanted to ask Mr. Cuomo to put in writing any promises of such changes.

Nothing came of the talk.

Ms. Perry was somewhat successful, however, in fending off Ms. Calcaterra’s efforts to be informed about all subpoenas in advance. She argued that Ms. Calcaterra had clearly been tipping off the governor’s office.

The three co-chairs, emails show, told Ms. Perry not to inform Ms. Calcaterra about subpoenas until just before they were served. Hearing this, Ms. Calcaterra accused the three of treating her like a “glorified secretary,” according to people involved with the commission.