Assuming that your dad had no basis in nondeductible contributions, the entire amount is taxable income to the beneficiaries (your children) and must be reported on the children's tax returns. (I assume that the amount of this unearned income to each child is more than $1,050, requiring each child to file.) This income might be subject to kiddie tax, calculated on Form 8615. If proper Forms 1099-R are not issued to the children, substitute Forms 1099-R with appropriate explanation will probably be needed.
As macuser_22 said, by operation of law the IRA became an inherited IRA upon the death of your dad, maintained for the benefit of your children as the beneficiaries, even though the IRA custodian might not have been aware of your dad's death. Also note that since these funds have been distributed and the beneficiary is not your dad's spouse, there is no option to get the money back into an inherited IRA.
Because the money was distributed late (depending on your dad's age, either RMDs or the 5-year deadline was missed), your children's tax returns should probably include Form 5329 requesting waiver of the 50% excess accumulation penalty.
