I believe in that situation, the income would be taxable to the client under the assignment of income doctrine. The client cannot change the fact the income belongs to her by issuing a 1099 to a third party.
The disclaimer may not resolve the issue either. The heir can disclaim the inheritance but can not dictate who it will go to, that is determined by the will or by law. Also, it appears the funds were accepted by her since they have already been transferred to an account under her name, so the window for disclaimer might already be closed.
As others have posted, the client can voluntarily gift a portion to her cousins in order to comply with her aunts request if she wishes. It would be her choice to make the gift after taxes, whether she takes it as a lump sum or by RMD over time. She is under no obligation to disclose how much the taxes are or what tax bracket she is in.