The petition's launch came after an official federal watchdog recommended that Conway be removed from her post, citing violations of The Hatch Act.
Half a dozen crew members had to be given a medical checkup after the plane was grounded.
The 21-year-old admitted to investigators he ingested meth prior to his flight to a rehab home in Malibu, California.
The lawsuit claims the cruise did not call the Coast Guard for a medevac nor did it turn back to Fort Lauderdale for medical help.
The ship was headed back to Port Everglades in Ft. Lauderdale, Florida, when an employee saw the crew member go overboard.
Hal Vaughan's trip was doubly special because he was recovering from a broken neck.
The ARA San Juan was lost with 44 crew aboard.
The M/Y Seanna is headed to Tahiti.
The officials are accused of violating an anti-corruption campaign law that prohibits government employees from engaging in politics.
The documents "shed light on how much taxpayers are paying for trips taken by the heads of the president's private business empire," the watchdog stated.
"Ms. Grisham likely engaged in political activity prohibited by law," the watchdog group states in a letter demanding an investigation.
"It may be a coincidence but if it is, it's a coincidence that could have easily been avoided," a CREW spokesman said.
"There must be 60 hotels in Washington. I don't believe the mattresses in the Trump hotel are any better. This is just weird," Richard Painter said.
The forms were referred to the Justice Department following a complaint by the watchdog group Citizens for Responsibility and Ethics in Washington (CREW).
It is "mind-boggling how someone can have that many errors and that many amendments and keep their job," a spokesman for a watchdog group said.
The former George W. Bush ethics chief is running for the Senate as a Democrat.
"Congress didn't confirm her for the gig. She isn't qualified. Has zero true diplomatic experience," a co-founder of the Democratic Coalition tweeted.
New documents show Steve Mnuchin took eight military flights "with no apparent justification," says government ethics advocates.
Kushner's office "ignored" Freedom of Information Act requests, an attorney for Food & Water Watch said.
Kushner's access to classified information even on a short-term basis "appears to represent a security threat," the complaint states.
Staff should beware of laws against using the government to help and hurt media companies, experts say.