OP says Client was the Beneficiary. If that is the case, cousins don't get a 1099R, nor do they get to roll any amount into any IRA if they get a gift from the Client. The IRA beneficiary designation form is the only thing that the 401K administrator is going to look at. They will not honor a will or trust document if the beneficiary designation has been made by the decedent.
There is the human side to this. The client wants to honor the Aunt's wishes, but that wish cannot trump what is a pretty cut and dry situation from a tax law standpoint.
Tom
Newark, CA