I honestly can't think of any sort of response that would affect her mother instead of Jamie.
Too bad, so sad. Jamie's mother's lack of parenting does not Stranger's problem make.
And Jamie's mother's lack of parenting does not make upsetting a child any less of a jerk move.
The fact that Jamie has a mother who has no concept of manners isn't the OP's responsibility. Specifically, the OP (or anyone else in this situation) is not responsible for protecting Jamie from the consequences of her mother's actions.
If we take the "I don't want to be a jerk to a little kid" position, then people like Susan can walk all over the rest of us, using their children as an excuse. "Oh, you're going to Disney World? Jamie will be so
disappointed of you don't take her. Oh, you won't? Look, she's crying, you jerk
Any jerkiness here is on Jamie's mother. If the OP upsets the child, she's merely passing on what she started. It's certainly unfortunate that it plays out that way, but a host in this situation isn't being a jerk at all saying "no."