Final answer:
The children most likely have an autosomal recessive disorder, such as Tay-Sachs disease or cystic fibrosis.
Step-by-step explanation:
The most likely genetic disorder that the children have is an autosomal recessive disorder. In this case, both parents have the genotype DD, which means they have a dominant allele for the trait. However, their children all have the disorder, indicating that they must have inherited two recessive alleles for the trait. Examples of autosomal recessive disorders include Tay-Sachs disease and cystic fibrosis.