the sons need to contact a Solicitor, though I have a feeling that if her name is on the bank book ( married or maiden name) then half of the money will be hers by right. The other half, I would presume, would be classed as the Estate of the deceased and be included in any will. If there is no Will then the Intestacy laws kick in which means the deceased's children would become beneficiaries of his Estate, including half of the money in a joint account.
Jenny, this is only a presumption and they would do well to see a Solicitor.