Jennifer Jones begged a court to be reunited with her kids but her appeal was rejected.
Two of the children have already gone back to their dad in Majorca and the other two – who have been in foster care while the court assessed the case – will now join them.
Jennifer, 46, hit the headlines last month when she was arrested after going on the run for five days with four of her five kids, aged between eight and 14, following a custody battle with their Spanish father, Tomas Palacin Cambra.
The children were found in the Gwent area - more than 50 miles away from Jennifer's home in Llanelli, Wales.
According to a newspaper report, Jennifer burst into tears when she learned of the Appeal Court's decision.
Lord Justice Thorpe sitting with Lord Justice Elias and Lady Justice Black dismissed the mother's appeal against an order last month that they should be returned.
A High Court judge must now make a new order for their return and that is expected to happen later this week or early next week.
Spanish courts granted Colonel Cambra custody of the children when his 12 year marriage to Jennifer ended in 2008. But they went to stay with their mum at her home in South Wales, in June for a summer holiday and did not return.
All four children started at schools in the town while Jennifer began legal proceedings in the family court to gain custody in a bitter battle.
In October the Family Division of the High Court ruled the children should be returned to their father.
But when Jennifer failed to return them to Spain Mr Justice Wood ruled the children should be taken from her home by police and social services. When they arrived Jennifer and her kids had disappeared.
Jennifer and her partner John Williams, 48, were held in custody and the children taken to foster carers.
Last month she was spared jail after being found guilty of 'flagrant breaches' of court orders to return them. But she may yet face prison after the judge - whose order she defied - sent the papers to the Attorney General.
Suggested For You
SUBSCRIBE AND FOLLOW
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements.Learn more