If you have the time, I would suggest that you read through this
blog post of mine, especially the second question about whether you need to call for a skill check, for my suggestions on how you can integrate the storytelling approach into the skill challenge framework.
Basically, just award the players automatic successes (without needing to roll a skill check) whenever they do something sensible or creative. For example, assuming you have decided that four successes are needed before three failures, the following could be automatic successes:
1. Pointing out that the rat child happens to be wearing same pink dress that Amy wore when she had vanished.
2. Pointing out that the rat child is holding the same porcelain doll that Amy had.
3. Asking the rat child to provide information that only Amy and her parents would know (you may also decide that this is especially convincing, and award two or more successes for this).
Apart from this, you might consider how the PCs might use various skills to overcome this challenge, for example:
Generic persuasion: Diplomacy, Bluff or Intimidate (Moderate difficulty)
Expert opinion - in this case, possibly citing similar documented historical cases or the signs and symptoms of magical transformation: History, Arcana or Nature (Moderate difficulty), possibly Heal (Hard difficulty)
Partly countering or dispelling the transformation: Arcana or Religion (first check at Moderate difficulty, subsequent checks at Hard difficulty).
Observation - these skills might not lead to successes in themselves, but might suggest avenues to explore that might lead to automatic successes, e.g. noting that the parents seem to recognize the rat child's dress and doll: Perception or Insight (Moderate difficulty)
Don't forget to think about what happens if the party fails. How does Amy react? Is there any way to undo the transformation before returning her to her parents? Can the PCs try again and if not, what prevents them from doing so?