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McALLEN, Texas (CNN) -- Attorneys for a Texas family accused Bridgestone/Firestone Corp. of putting money over safety Monday, while lawyers for the tire maker blamed Ford Motor Co. for the accident that left one woman in a wheelchair for life.

It is the first time a tire tread separation injury lawsuit against the troubled tire maker has proceeded to trial. All other tread separation claims have been settled out of court.

"In this case you will hear stories of a company that has lied, misrepresented the quality of its tires and breached the trust of American consumers," said plaintiff attorney C. Tab Turner in his opening statement. "Firestone is a corporation that puts money over the safety of its customers."

Firestone attorneys aimed their attack at Ford Motor Co., blaming "fundamental design problems with the Ford Explorer" for the accident.

"Tread separation should be nothing more than an inconvenience, not cause a terrible accident," the company's attorney, Knox Nunnally, told the court Monday.

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Marisa Rodriguez was a rear-seat passenger in the family's 1998 Ford Explorer when it rolled over in Reynosa, Mexico, on March 9, 2000, leaving her permanently wheelchair-bound.

Also in the car were her husband, Joel, 42, and their 3-year-old son. Her brother-in-law, Jorge Rodriguez, was driving the Explorer when the right rear Firestone Wilderness AT tire separated and the vehicle rolled over. All three were injured, though not as severely as Ms. Rodriguez.

The Rodriguez family is asking for $1 billion in damages. They have already settled a lawsuit against Ford Motor Company for an undisclosed amount.

The accident occurred just five months before Bridgestone/Firestone Inc. announced it was recalling 6.5 million 15-inch AT, ATX, and ATX II tires manufactured at Firestone's Decatur, Illinois, plant, where the Rodriguez's tire was made.

Bridgestone/Firestone spokeswoman Jill Bratina said the company has the deepest sympathies for Rodriguez family, but said the Ford Explorer's design is to blame for their accident. She said Firestone tires are safe and that tread separation can occur in any brand of tire.

"After a tread separation, a driver of a vehicle should be able to pull over to the side of the side of the road and change the tire, she said. "Unfortunately in this case, and with the Ford Explorer, that was not possible, Ford Explorers are designed in such a way that there can be a loss of control, as happened in this particular situation."

U.S. District Judge Filemon B. Vela, Southern District Court of Texas has said the case will not last more than two weeks.

Recall of more Firestone tires expected

The trial comes as the National Highway Traffic Safety Administration is expected to seek a mandatory recall of more Firestone tires. NHTSA officials have said they would formally announce their request sometime this month -- the one-year anniversary of the company's massive recall.

The NHTSA has documented 203 deaths and more than 700 injuries linked to tread separation rollover accidents involving the tires.

Lawyers for the family were trying to have the case moved back to state court last week, but said they were pleased with the judge's ability to get the suit to trial.

"We're happy on the anniversary of the recall that we're now ready to proceed with the case," said Ricardo Garcia, one of the attorneys representing the Rodriguez family.

Attorneys for the tire-maker had asked Vela to recuse himself from the case because his son, Filemon Vela, Jr., represents a plaintiff in a suit against Firestone. Vela refused.

Judge Vela did not issue a gag order in the case, but warned attorneys that he did not want the case tried in the media and "invited" both parties to not talk to the press about the case.

Ford, Firestone face hundreds of lawsuits

Both Firestone and Ford face about 400 lawsuits combined, both in federal and state courts.

Bridgestone/Firestone has settled more than 200 tread separation lawsuits involving its Wilderness AT tires, said spokeswoman Jill Bratina. The company announced Sunday that no settlement was reached in the Rodriguez case.

Firestone's lead lawyer, Knox Nunnally, is expected to focus on the Ford Explorer in the case. Bridgestone/Firestone insists a design flaw in the Explorer made it more vulnerable to rolling over, contributing to the many accidents.

In May 2001, Ford announced it would replace another 13 million Firestone tires in addition to the earlier recall, citing unusually high failure claims rate data.

It was at that time that Firestone announced it was severing its nearly 100-year-old business relationship with the auto maker

-- CNN Detroit Field Producer Carol Yancho and Correspondent Ed Lavandera contributed to this report.