In this situation as the gambler in question, his parents will still have some trust in him as he is their son and if it is only the first time that he has done that then there may not be reason not to distrust him. They may not keep such money with him but the issue of trust have not gone with them, they are still family.

If I'm in his shoes then I would make sure that I make them realize it was a mistake that I relied on gambling to double the money. I will let them know it will also be in their own benefit if the money was increased as a result of the gambling risk taken. Hence every wrong has somethings you need to do to placate others and I will humbly plead mistake.