“I believe everybody should have that American dream, coming here and working hard for your family and doing the right thing,” Ms. Rodriguez, whose parents came to New York from Puerto Rico, said in a recent interview. “I do not accept the ones that are coming over with the criminal record long as ever and doing the crimes here and killing our kids.”

Law enforcement officials say that not every MS-13 member is an undocumented immigrant, but that the gang recruits from a base of unaccompanied Central American minors who entered the country illegally.

Since Sept. 13, the police in Suffolk County have arrested more than 90 MS-13 members, with many in federal custody as officials gather evidence to charge them under organized crime law. The gang, also known as La Mara Salvatrucha, was responsible for the killings of 11 people in Suffolk County last year, the police said. It was not clear if the murders would be included in the charges.

As part of Mr. Trump’s executive orders, he directed the Immigration and Customs Enforcement agency to expand its gang-fighting crime initiative. Even before the orders, Suffolk County had rejoined a joint gang task force with the F.B.I. and increased its own street patrols last fall.

But to Ms. Rodriguez, it is not enough.

“I told the Third Precinct, I want you to be pressing on this,” Ms. Rodriguez said, referring to the police precinct that covers Brentwood. “If you see three, four individuals in front of a store, I want you to roll up on them and see ID and if they don’t have ID, then you bring them in.”

Even as Mr. Sini has tried to make the police department more transparent within the community, he does so amid Suffolk County’s tangled history with Latino immigrants.