I'm kind of confused about this. As I was scrolling through Facebook this evening I came across a picture of my friend's daughter. It's been a while since I've last seen her, and now she's all grown up and beautiful. I wanted to leave a nice comment on her photo telling her (my friend) how beautiful her daughter turned out to be. I'm aware that the phrasal verb Turn out can be used for people just okay, but what if I wrote the sentence this way: Your daughter is turning out beautiful/beautifully would that also work?
Beautiful is an adjective, not an adverb. So using it in that construction would not be entirely normal—although it's the sort of thing that people might say informally.
In the same construction, you would use the adverb more often:
Your daughter is turning out beautifully.
However, that's a little odd because it sounds like a description of a project or a meal rather than of a person.
Better would be to use a construction that makes more idiomatic use of the adjective.
Your daughter is turning out to be beautiful.
Your daughter is turning out to be a beautiful woman.
You might also replace the verbal phrase turning out with something else:
Your daughter is turning into a beautiful woman.
Your daughter has become quite beautiful.
I don't find the phrasal verb "turn out" suitable to use in your case. It is the same as saying: "I was seeing your daughter as ugly the whole time until now when she turned out to be a pretty girl".
I suggest you say:
Your daughter has grown up to be such an elegant lady.
So that it won't appear as a flirt or an insult.