The same result would occur if the OP does what you suggested and returns mom's mail. Mom still will not have her money when its needed to pay the bills, and in fact, returning it rather than passing it on would create a bigger delay in the funds being available to mom.Other than the issue of op ststing she doesn’t intent on blindly handing the annuity check to the sister, I can understand why she wouldn’t want the ,others mail sent to her. It appears the sisters don’t get along. I can see the other sister claiming op has destroyed mother’s mail if it doesn’t show up at sisters house, or even if it does and sister wants to claim it didn’t.
Op needs to contact her local postmaster and inquire if she can have all of,the mothers mail intercepted and not delivered to op’s home.
If that is not possible, I have no problem with op stamping ALL mail:
No such addressee at this address
And give it back to the mailman.
Sister can then change the address with the various senders and all will be well with the world
Intercepting your mothers mail and keeping it is illegal. You do not have the authority to decide what happens to your mothers annuity payments and could actuslly be liable for damages if retaining the payment results in your mother owing additonal money by not having the funds available to pay a debt.