Your daughter is using it in a linguistic context that she's learnt, and probably has not had the experience with the more general meaning that you understand.
Analogy is explaining one thing in terms of another to make it more easy to understand (in your definition).
Analogy is expressing one thing in similar terms to another to regularise the system (in your daughter's definition). This is a specific definition in linguistics.
That is, where English used to use the terms /help, holp, holpen/, it now uses /help, helped, helped/, in analogy to the verb "yelp".
You could explain to your daughter that 'analogy' has more than one meaning - but that the meanings are similar.