The only difference that occurs to me is that "teenage" usually has a broader meaning.
The adjective "teenage" can mean either "in one's teens" or "pertaining to/characteristic of teenagers". But "teenaged" is in most cases limited to the meaning "in one's teens" (and this is the way I would use it).
i think "teenage daughter" is correct in form, and maybe you just have to put a dash/hyphen in the word "teen-aged" to make more grammatically correct.