In this sentence, the middle part "--who love you" is an attributive clause which depicts "the people", but how to explain the latter clause? Is it an emphatic sentence? Could someone explain the whole sentence in a detailed way? Much thanks.
A similar sentence: "It's what we have we don't cherish." I think it's what's known as "cleft sentence". The latter part is a dependent clause. Rewritten as a regular sentence it would be "You're the hardest on the people who love you". You can take any simple sentence that has an object and rewrite it as a cleft one by starting with "it is/was".
The last part is usually connected by "what", "which", "that" or "who/whom", but such a word can be omitted, like in your case.