Legal representatives say John and Mary Brown (names changed) legally adopted 'Dan' and 'Tom' in 2013 and the youngsters both had "various behavioural issues".
According to the Christian Legal Centre (CLC), Tom was "in a fairly heightened mood" on the day of his second SAT exam when he reached for the steering wheel during a drive to school.
In that moment, Mrs Brown pushed Tom back, the CLC says.
The organisation claims Tom and Dan reported what happened, along with "fabrications" to the school, when the head teacher rang social services and the police, and the boys were taken away.
It's understood Tom and Dan are now living in different places, leaving their parents "absolutely devastated".
The CLC has revealed two judges at the Royal Courts of Justice, Lady Justice King and Lord Justice Simon, have today allowed the appeal and have ordered a retrial of the case.
Speaking after the decision, Chief Executive of the Christian Legal Centre Andrea Williams said: "We are relieved and delighted that the Court of Appeal has ordered a retrial of this case, but the battle is not over. We will continue to pursue justice for this family."
Mrs Brown said: "We want our boys back and we will do all we can to bring them home."
Her husband added: "We are grateful to the Christian Legal Centre team for their continued support."
It's understood the primary reason a family court judge gave for refusing to return the children to their adoptive parents was that a psychologist's report didn't recommend the children's return.
Andrea Williams said: "We have been unable to expose the gross injustice in this case because of the secrecy surrounding the family courts.
"This case is the tip of the iceberg.
"These wonderful parents have been greatly disrespected. The state seemed not to treat them as parents because they were adoptive parents.
"The objective evidence of the boys' progress over years seems to have been dismissed.
"Such a flimsy rationale for the removal of children from a loving home is appalling."
In granting the appeal, Lady Justice Black reportedly ruled that there should be a review as to whether the judge at the family court had taken the right factors into account when deciding the boys' future and whether he had failed to give proper weight to the good parenting that had been given to the children for three years prior to their forced removal.
The Christian Legal Centre has seen a growing number of family cases over the last few years.
Commenting on this case, Andrea Williams added: "We are seeing a worrying trend, whereby Christian parents are being treated with suspicion because of their faith.
"The 'Browns' were treated as if they were not the 'real' parents.
"Their views on disciplining the children and taking them to church were wholly disrespected by the social services and the children themselves tragically taken away.
"It is time for a change regarding the secrecy surrounding child courts.
"Their secretive nature means that injustices can be covered up, and it is time for this to be reviewed.
"We are grateful for the opportunity this appeal provides to shed light on a system that has perpetrated gross injustices against loving and fully competent parents."