Equusearch found additional vehicles, the group said Thursday, but none fit the description of Monette's car.
Enclade said she believes someone has taken her daughter -- a new aunt -- against her will.
"Terrilynn was supposed to be the baby's godmother, and I know she wouldn't have just left on her own like that," she said.
A star teacher
In her first year of teaching second grade at Woodland West Elementary School, Monette turned one of the lowest-performing classes into one of the highest achieving.
"She is wonderful, she is vibrant. She is determined. She holds her students to the highest of expectations," Principal Amy Hoyle said. "She is very loving with her students. They are a family."
Enclade said she and her daughter usually speak every day, and it's extremely uncharacteristic for Monette to drop out of sight.
Friends and family have erected a billboard in downtown New Orleans seeking help in finding Monette. They also created a Facebook page.
"It hurts," Monette's aunt, Sheryl Bennett, told CNN affiliate WDSU. "There's a lot of danger out here."
But in her 2011 video, Monette said she had no qualms about starting her teaching career in New Orleans.
"I absolutely do not regret my decision to move out here. Becoming a teacher in New Orleans is one of the best decisions I've ever made in my entire life."