You two beneficiaries should complete the parent’s 2019 RMD. You are jointly responsible which means that the total can be distributed in any combination between the two of you. If one of you needs the money, that beneficiary can complete the entire year of death RMD and the other need not distribute anything.
Neither of you can take a distribution or transact from the actual inherited account because you each need to supply required data (contact info SSN, copy of death Cert) in order to establish your own separate inherited IRA and for the custodian to discuss anything with you. Custodians do not want to have multiple SSNs on a single IRA, so almost all of them will set up separate inherited IRA accounts for each beneficiary. No reason to delay. Once these inherited IRAs are established, the year of death RMD can be distributed. Obviously, this will require some communication and coordination between the two of you. Every so often one or more of several beneficiaries is dysfunctional. In that case, the responsible one need only take THEIR share of the year of death RMD as the IRS is not going after one beneficiary for the failings of others. Any distribution to a beneficiary will be followed by a 1099R and that beneficiary (not the estate) reports the taxable income. The estate (executor) is only formally involved in the account if the estate is the actual beneficiary because the owner failed to name one.
Your general observations are correct. Starting next year each beneficiary is solely responsible for their own calculated beneficiary RMD which is due by 12/31/2020.
A QCD can be taken from a beneficiary IRA, but ONLY when the beneficiary reaches 70.5.