At first glance, the “as rapidly” would seem to be a contraction in terms. However (IMO), it appears that it is more of a general term, to which distributions from
individual accounts are exempted.
Q&A 5 of §1.401(a)(9)-2 states
QUOTE
Q-5. If distributions have begun to an employee during the employee’s lifetime (in accordance with section 401(a)(9)(A)(ii)), how must distributions be made after an employee's death?
A-5. Section 401(a)(9)(B)(i) provides that if the distribution of the employee's interest has begun in accordance with section 401(a)(9)(A)(ii) and the employee dies before his entire interest has been distributed to him, the remaining portion of such interest must be distributed at least as rapidly as under the distribution method being used under section 401(a)(9)(A)(ii) as of the date of his death. The amount required to be distributed for each distribution calendar year following the calendar year of death generally depends on whether a distribution is in the form of distributions from an individual account under a defined contribution plan or annuity payments under a defined benefit plan. For the method of determining the required minimum distribution in accordance with section 401(a)(9)(B)(i) from an individual account, see §1.401(a)(9)-5. In the case of annuity payments from a defined benefit plan or an annuity contract, see §1.401(a)(9)-6T.
For your question, the “individual account” rule under §1.401(a)(9)-5 would apply
Q&A 5 of §1.401(a)(9)-5 states
QUOTE
For required minimum distributions after an employee’s death, what is the applicable distribution period?
A-5. (a) Death on or after the employee’s required beginning date. If an employee dies after distribution has begun as determined under A-6 of §1.401(a)(9)-2 (generally on or after the employee’s required beginning date), in order to satisfy section 401(a)(9)(B)(i), the applicable distribution period for distribution calendar years after the distribution calendar year containing the employee’s date of death is either –
(1) If the employee has a designated beneficiary as of the date determined under A-4 of §1.401(a)(9)-4, the longer of --
(i) The remaining life expectancy of the employee’s designated beneficiary determined in accordance with paragraph ©(1) or (2) of this A-5; and
(ii) The remaining life expectancy of the employee determined in accordance with paragraph ©(3) of this A-5; or
(2) If the employee does not have a designated beneficiary as of the date determined under A-4 of §1.401(a)(9)-4, the remaining life expectancy of the employee determined in accordance with paragraph ©(3) of this A-5.
Therefore, since the children (obviously) has a longer life-expectancy than the participant, they would take distributions over the “The remaining life expectancy of the employee’s designated beneficiary”
Regarding the separate accounting issue-
§1.401(a)(9)-8 states A-3.
QUOTE
For purposes of section 401(a)(9), separate accounts in an employee’s account are separate portions of an employee's benefit reflecting the separate interests of the employee’s beneficiaries under the plan as of the date of the employee’s death for which separate accounting is maintained. The separate accounting must allocate all post-death investment gains and losses, contributions, and forfeitures, for the period prior to the establishment of the separate accounts on a pro rata basis in a reasonable and consistent manner among the separate accounts. However, once the separate accounts are actually established, the separate accounting can provide for separate investments for each separate account under which gains and losses from the investment of the account are only allocated to that account, or investment gain or losses can continue to be allocated among the separate accounts on a pro rata basis. A separate accounting must allocate any post-death distribution to the separate account of the beneficiary receiving that distribution.
Assuming these requirements are met, each beneficiary would be allowed to use his/her own life expectancy.