I have great confidence that China will properly deal with North Korea. If they are unable to do, the U.S with its allies will.?

I have confidence ....這句的結構是simple sentence：主詞＋及物動詞＋受詞
受詞是「名詞片語」：confidence of xxx，但因that子句（名詞子句）通常不受介系詞的約束，所以前面的介系詞遭到強制刪去，只剩下that子句。請看類似的句子：
He betrayed my confidence "in" him.
He betrayed my confidence that he would do it well.

We had every confidence "of" success.
I had confidence that he would succeed.

名詞片語是由名詞＋介系詞＋（代）名詞組成時，後面的介系詞＋（代）名詞是一個修飾語，修飾它前面的名詞。

If they are unable to do, the U.S. with its allies will.是complex sentence: 副詞子句（當主句述部的修飾語，提供條件）＋主要子句

The main clause : "I have great confidence" is being joined and introduced by the noun clause: "that China will properly deal with North Korea." in here "that" acting as conjunction in between the main clause And then being followed. by "If they are unable to do, the U.S. with its allies will", here acts as conjunctive clause to indicate that the condition will be fulfilled. YIp