Thae description is not quite correct.
The word but is usually a coordinator (sometimes called a coordinating conjunction). When it occurs between two full clauses, as it does here, it is always a coordinator. This means that the two clauses in the sentence are of equal status. We don't regard one of them as the main clause and the other as subordinate. Rather, we have a coordination of main clauses:
- [Today I am starting a diet] but [first I will eat all the children’s chocolate they have left over from Easter].
However, the Original Poster is correct that the second coordinate (the second clause) contains a bare integrated relative clause (also known as a bare restrictive relative clause), the antecedent for which is the noun chocolate:
- chocolate [they have leftover from Easter]
Notice that this relative clause is itself a subordinate clause. So the best description might be:
The sentence consists of a coordination of two finite clauses, the second of which contains a subordinate, restrictive relative clause modifying the noun chocolate.