Answer: The comma rule that the sentence provided breaks is "Use a comma to set off a phrase or clause at the beginning of a sentence".
Explanation: The sentence provided is made up of a subordinate clause and an independent clause. The subordinate clause is "Although she loved her parents", while the independent clause is "Sarah was eager to leave for college and be independent". Punctuation rules state that, when a subordinate clause is placed at the beginning of a sentence, a comma must be included between the subordinate clause and the independent clause. In that way, as the sentence provided does not include a comma between the subordinate clause and the independent clause, this sentence breaks the rule "Use a comma to set off a phrase or clause at the beginning of a sentence".