我觉得如果你知道自行车和单车的区别，也就明白嵌入句和插入语的区别了，只是叫法不同而已，本质上是一回事。你的句子中do you think 应该不算嵌入句。你自己想出的句子：What do you think what we should do?  让我说是Chinglish. 

      So it's no use making any grammatical analysis of your sentence. You must pay particular attention to the way native speakers use English rather than some queer technical terms. Please take my word for that!