Brief update: I mailed her with a "Gee I sure hope it didn't go to the wrong address" message, and predictably she replied, "Oh, I messed something up because it got returned to me so I posted it again last week." I think she's lying. If there wasn't enough postage on it, I would have had to pay the difference. If it was mis-addressed it wouldn't have been returned to her so quickly.
I guess this does belong in toxic families after all, but I just wanted to give you all an update and say thanks for all the kind replies. And I won't be acknowledging her birthday in January, nor will I be wishing her a Merry Christmas. It doesn't mean anything to her anyway.