I think that you have an inaccurate description of the circumstances. I suspect that the trust is the beneficial owner of the inherited IRA and you are a beneficiary of the trust (and it's not your inherited IRA), but you disclaimed this interest in the trust and, under the terms of the trust, this allows this interest to be distributed from the trust to your children. Otherwise, if you were the beneficial owner of the inherited IRA, the trust would not be involved at all and no distribution should have been made to the trust.
The income passed through to trust beneficiaries on Schedules K-1 will be taxable income to the beneficiaries and the trust will take a deduction for Distributable Net Income. Because tax withholding on distributions paid to the trust are not permitted to be passed through to trust beneficiaries on the Schedules K-1, the trust will need to receive a refund of any excess taxes withheld on distributions paid to the trust and then distribute this cash to trust beneficiaries. Yes, it would have been simpler to decline tax withholding on distributions paid to the trust.
