Their daughter, Jayda, had been in the care of the local authority since her birth in October 2010, at a time when her parents were still facing criminal charges relating to her brother.
The local council refused to return Jayda because social services remained convinced her parents may have been responsible for her brother's death.
The couple then endured a four-week hearing at the High Court during which the same accusations were levelled at them.
In a landmark ruling made public on Thursday, they proved their innocence for a second time and had their toddler daughter returned to them earlier this month after nearly 18 months.
Legal experts said their case would transform the way in which so-called shaken-baby cases were treated by the courts.
Sitting at the court's Family Division in London, Mrs Justice Theis ruled that the allegations made against them had not been proved.
Care proceedings in relation to Jayda have been dismissed and she has returned to live with her parents.
"I am aware that some of the medical issues considered in this case have generated debate, both within and outside the medical arena," she said.
"Despite the parents' youth and the fact the pregnancy was unplanned, Jayden was very much a wanted baby."
The couple's extraordinary case can be reported for the first time after a judge lifted restrictions preventing the couple from speaking publicly about their protracted battle in the family courts to win back their child.
On Thursday night the couple, from Islington, north London, called for an inquiry into their "agonising" treatment at the hands of social services, the NHS and the police.
"There are medical staff who we believe should be disciplined at an inquiry," Mr Wray told the Daily Mail.
"I think these medical experts who judge parents are dangerous people. They base much of what they say on opinion rather than fact.
"We feel we were treated very poorly by the state authorities involved in investigating our case. We were viewed as guilty from the outset."
His partner added: "The doctors and the police made allegations against us without any real proof."
Jayden was found to have brain damage and multiple fractures after he was taken to Great Ormond Street Hospital in July 2009 after he began suffering seizures and refusing to feed.
His life support machine was switched off three days after admission. His parents maintained their innocence, saying Jayden had rickets and his collapse was due to "natural causes".
They were cleared after more than 60 prosecution and defence medical experts disagreed on the cause of death.
The prosecution offered no evidence on the murder charge and not guilty verdicts were returned. Judge Stephen Kramer QC ruled that the charge of causing or allowing the death of a child should be discontinued.
But the High Court case brought by Islington Council was that Jayden had "died as a result of inflicted trauma caused to him whilst in the care of the parents".
It was further alleged that he suffered "a number of fractures that, despite having rickets, were caused by non-accidental injury".
At the centre of the issue was an increasingly bitter dispute between different medical experts, who disputed which combinations of injuries should be used to infer abuse.
The local authority had relied on the "medical evidence of fact and opinion to undermine the credibility of the parents".
In Thursday's judgment, Mrs Justice Theis ruled: "The issues surrounding vitamin D deficiency have dominated this hearing.
"Evidence has been given that it is on the increase, leading possibly to an increase in congenital rickets.
"The identification of it is not easily done, as this case so graphically demonstrated."
She said the case had generated a considerable amount of publicity at the time of the criminal trial.
"I am aware that some of the medical issues considered in this case have generated debate, both within and outside the medical arena," she said.
"It is important to remember that my conclusions are entirely related to this case. Despite their differences of opinion, all the medical experts agree this case is extremely complex.
"By their very nature, cases such as this are very fact-specific and great caution should be adopted in using any conclusions I reach to support any wider views outside the very specific facts of this case."
Outside court Ann Thompson, of law firm Goodman Ray and who acted for Ms Al-Alas in the family case, said the judgment would "make a huge difference to future cases".
"It is historic and it will make courts assess the issue of vitamin D deficiency much more carefully," she said.
"It is an important judgment, especially given the proliferation of vitamin D deficiency in this country at the moment and the lack of research on the implications of this, which is an area of research that the judge has strongly encouraged.
"Nothing is as sad as the death of a child. But for these parents, the nightmare went on and on."
Islington Council declined to comment.
