首先你写的这个句子有错误，错误就出在第三个that 引导的这句话that they are among these are life, liberty and the pursuit of happiness．that 后应该去掉they are. 请你再查查《独立宣言》的原文，仔细检查一下，以后提问题起码关键部分要准确。

我觉得这个that 引导的句子应该看做同位语从句。作者为了强调三个权利，从句采用了倒装的写法，把among these 前置了。如果是定语从句，应该这样写：that are life, liberty and the pursuit of happiness 或 among which are life, liberty and the pursuit of happiness.