A "woman with means" who was arrested at a Mexican beach resort city with her fugitive teenage son who invoked "affluenza" as a defence after killing four people in a drunken-driving wreck has complained about the conditions of her Texas jail cell, a sheriff said Friday.

"She expressed a slight displeasure about her accommodations, and I told her this was a jail and not a resort," Tarrant County Sheriff Dee Anderson said at a news conference.

Tonya Couch, 48, and her 18-year-old son Ethan Couch, have been the objects of derision since Ethan was sentenced to probation, rather than jail time, for the 2013 wreck.

During his trial for the 2013 crash, a psychologist testified on Couch's behalf that he had "affluenza," meaning he had lost the ability to recognize right from wrong after being spoiled by his wealthy family. The diagnosis, which is not recognized by the American Psychiatric Association, was widely ridiculed. 

The case drew renewed attention when the mother and son fled to Mexico after a video surfaced that appeared to show Ethan Couch, fresh from a rehabilitation centre, at a party where people were drinking. If Couch drank alcohol, he violated the terms of his probation.

Tonya Couch made an initial appearance in a Texas courtroom Friday on a charge of hindering the apprehension of a felon. She did not enter a plea because her attorney was not present for the arraignment.

Tarrant County Judge Wayne Salvant advised Couch of the charge against her and asked if she understood. The mother, wearing a yellow jail jumpsuit, said she did.

$1M bond set

Salvant set bond at $1 million and Couch's attorney, Stephanie Patten, filed a motion asking for the bond to be reduced.

"We think anything $25,000 or under would be fair," Patten told reporters.

Anderson said he opposed a bond reduction because Couch is "a woman with means who can get out of the country with the right connections."

Couch told the judge that she surrendered a temporary passport in Los Angeles, where she was deported from Mexico last week.

Authorities believe the mother and son fled Texas together in November as prosecutors investigated whether the teenager had violated probation. They were arrested at an apartment complex in Puerto Vallarta late last month.

Mexico US Deadly Wreck Affluenza

This Dec. 28, 2015, file photo, released by Mexico's Jalisco state prosecutor's office shows who authorities identify as Ethan Couch after he was taken into custody in Puerto Vallarta. (Handout/Associated Press)

Ethan Couch was driving drunk and speeding near Fort Worth in June 2013 when he crashed into a disabled SUV, killing four people and injuring several others, including passengers in his pickup truck.

He pleaded guilty in juvenile court to four counts of intoxication manslaughter and two counts of intoxication assault causing serious bodily injury and was sentenced to 10 years' probation.

Couch is being held at an immigration detention centre in Mexico City after winning a delay in deportation, a ruling that could lead to a drawn-out court process if a Mexican judge decides Couch has grounds to challenge his deportation based on arguments that kicking him out of Mexico would violate his rights.

Such cases can take anywhere from two weeks to several months, depending on the priorities of the local courts and the actions of defense attorneys, according to Richard Hunter, chief deputy for the U.S. Marshals Service in South Texas.

With files from Reuters