Will the judge grant custody to the mother or to the children's grandfather, knowing that the children are infants and the mother is a widow and has the right to custody?

Guardianship over an orphan is of two types: guardianship over the person (wilayat nafs) and guardianship over the wealth (wilayat mal). The mother has no share in either of these, unless she was appointed as a guardian by the father. As for the mother's right, it is only custody (hadanah). She must refer the matter to a Muslim judge to determine the legal guardian for the two children, because the order of guardians after the father is a matter of disagreement among scholars, and the ruler's judgment resolves disputes and considers what is in the best interest.