You're absolutely right! Subordinating conjunctions connect two clauses where one is dependent on the other. In your example, "They are happy because their life is perfect," the independent clause ("They are happy") can stand alone as a complete sentence, while the dependent clause ("because their life is perfect") cannot.
This is a great way to distinguish between independent and dependent clauses. Another example could be: "She stayed inside because it was raining." Here, "She stayed inside" is the main clause, and "because it was raining" explains the reason but cannot stand alone.
This is a great way to distinguish between independent and dependent clauses. Another example could be: "She stayed inside because it was raining." Here, "She stayed inside" is the main clause, and "because it was raining" explains the reason but cannot stand alone.