"Menantu saya cantik dan tinggi."
"My daughter-in-law is beautiful and tall."
It's a different sentence, that's why it's marked wrong.

"Menantu saya yang cantik dan tinggi."
You are right that you could back-translate the current sentence as a phrase instead of a complete sentence.
"My daughter-in-law who is beautiful and tall, ..." (phrase)
"My daughter-in-law is the beautiful and tall one." (sentence)

Compare the next two questions and the answers:
"Bagaimana menantu kamu ?" (How is ...)
"Menantu saya cantik dan tinggi."

"Yang mana menantu kamu ?" (Which one is ...)
"Menantu saya yang cantik dan tinggi."

Your translation is an answer to the first question.
This sentence is an answer to the second question.

Why is the "yang" in there?

Without "yang" the sentence has a different meaning.
"yang" is used to refer to something that is previously mentioned.
As you correctly pointed out yourself, it can even be back-translated as a phrase instead of a complete sentence.
As a phrase, "yang" refers to the noun phrase "menantu saya".
As a sentence, "yang" also refers to the previous sentence/question.