I contacted Live Chat and they said:
* "I will add rush delivery notes for you"
* "we will do the rest for you with a rush delivery"
Then it was the Friday before Mother's Day and I got a notification the item will be delivered some time the following week.
I contacted Amazon Live Chat again:
* We never promised you a specific delivery date.
That's completely true, Amazon.
Turns out "I will add rush delivery notes for you" and "we will do a rush delivery" is a meaningless customer service thing you can say like, "your call is important to us".
This doesn't require taking any action to expedite the order or, failing that, telling the customer who is asking you about delivery for Mother's Day that they need to order a different product if they expect it to arrive in time.
So basically Amazon Customer Service is now no better or worse than any generic chat bot you can use to accomplish (or fail to accomplish) the same thing.
It's my own fault: if an item had no delivery date the week before Mother's Day, I should have canceled earlier.
What problem were they unable to resolve?