Which is the correct sentence?

These are questions of style, and neither sentence can be said to be wrong. When I include a sentence withing a sentence, in quotation marks, I capitalize the initial word, and end it with a "full-stop" punctuation mark, assuming that we refer to a complete sentence. Personally, I would not use "answer of," but only "answer." Finally, I would not put a period after the end of a quoted sentence which ends in a full stop (such as the exclamation mark after "yes" in your daughter's sentences.

EDIT: An exclamation point (!) or a question mark (?) is a full stop, just as a period is.

"Is this wrong?"

"Yes!"

Thanks, Setanta and Punkey.