Bahamas Sen. Pleasant Bridgewater was also arrested and charged with conspiracy to extort.
Each has pleaded not guilty and is free on bail. Bridgewater later resigned from her office.
The extortion charges involve the pair's alleged plan to release a document if Travolta and his wife, actress Kelly Preston, did not pay them $25 million.
The paperwork they allegedly threatened to release is a "refusal to transport," which someone would sign when refusing emergency medical services, thereby releasing first responders from liability.
But police said no such document was ever signed in this case.
A police officer testified Tuesday that Travolta signed the release because he initially wanted his son taken to the airport instead of the hospital.
Outside the courthouse on Monday, Bridgewater's attorney told APTV that without Travolta, there is no case.
"He has to be here, he has to come and give evidence," said Murrio Ducille. "Without him, the prosecution cannot get off the ground, because he is the complainant."
Lighthourne's defense attorneys have asked the court to order the prosecution to turn over documents, including the autopsy report, the statement from Travolta's nanny and phone records, which they say they have not yet received, despite repeated written requests.
Defense counsel Carlson Shurland had already expressed his concerns about the fairness of his client's trial, earlier in the year.
"Our anxiety has to do with all of the adverse publicity that this case has been getting," said Shurland in a February interview with The Freeport News. "In light of all of that publicity we doubt seriously that we will be able to find an impartial jury in The Bahamas simply because everybody has an opinion."
One party that has shied away from all publicity until recently is the Travolta family.
John Travolta did not join his co-stars over the summer in promoting "The Taking of Pelham 1 2 3." Actor Denzel Washington told "Good Morning America" in June that his co-star was still in a "tough situation."
Travolta posted a message to his colleagues on his Web site at the time: "Their unselfish efforts have allowed my family the additional time to reconcile our loss."
And last month, Preston decided to pull out of the October women's conference hosted by California first lady Maria Shriver, where she was to host a session on grief and resilience.
In a statement to People magazine, Preston explained her withdrawal: "I am sorry, but I truly believed that I could do it. Otherwise I never would have said that I could. But I am still deeply in the process of healing, and it's just too soon."
The family's first public appearance was only two weeks ago when the couple and daughter Ella attended Disney's D23 Expo to promote their upcoming film "Old Dogs."
Travolta and Preston are not the first celebrity targets of alleged extortion plots. Rob Lowe, Bill Cosby, Tom Cruise, Bruce Willis, Steven Seagal, basketball great Michael Jordan, model Elle Macpherson, singer Celine Dion's husband Rene Angelil and the late Michael Jackson have all been the target of alleged schemes to extract thousands or millions of dollars, though none of these cases involved the death of a child.
The Bahamas courthouse where the trial is scheduled is no stranger to high-profile cases. Almost three years ago, it was the scene for the official inquest after the death of Daniel Smith, the son of the late Anna Nicole Smith. The Associated Press contributed to this report.