What do you mean by "processed a distribution to claim the IRA on behalf of my mother-in-law's estate?" An inherited IRA is not permitted to be moved by distribution and rollover. Do you mean that your father-in-law's IRA was moved by trustee-to-trustee transfer to an IRA for the benefit of your mother-in-law's estate?
Assuming that the IRA was moved to your mother-in-law's by a proper trustee-to-trustee transfer, I suspect that your father-in-law's year of death RMD can be taken by the estate of your mother-in-law (likely with this income to the estate passing to the same beneficiaries of your mother-in-law's estate as would the inherited IRA) before transfer of the remainder to the beneficiaries of your mother-in-law's estate, or the year of death RMD could be taken by these beneficiaries after transfer of to inherited IRAs for the benefit of these beneficiaries. The IRS is appears to be mainly interested in seeing that the year-of-death RMD is taken. If the beneficiaries of the estate want to realize the income from your father-in-law's year-of-death RMD in different proportions than they would from distributions of that income from your mother-in-law's estate, the year-of-death RMD would have to be completed after transfer of the inherited IRA to their separate inherited IRAs. If the estate receives the year-of-death RMD, that likely means that the estate will need to file and estate income tax return, Form 1041 (which may or may not already be required for other income to the estate).
The beneficiaries of your mother-in-law's estate are successor beneficiaries, subject to the 10-year rule. Because your father-in-law died after is required beginning date for RMDs, according to the proposed IRS regulations they would also be subject to annual RMDs. I'm not sure if those are based on the beneficiaries' separate life expectancies (assuming that the IRA is split and transferred from your mother-in-law's estate to separate IRAs for the benefit of the beneficiaries of your mother-in-law's estate by the end of 2022) or on your mother-in-law's life expectancy, but I think the latter. (Taking them based on your mother-in-law's life expectancy would certainly be sufficient assuming that the estate beneficiaries are younger.) We are still awaiting the final regulations from the IRS. The beneficiaries of your mother-in-law's estate (or the estate itself if the inherited IRA is not transferred to beneficiaries) must also complete your mother-in-law's beneficiary RMD by the end of 2022.
Form 5329 requesting waiver of the 50% excess accumulation penalty needs to be filed by whatever entity (or entities) receives this distribution.
