Dependent clause *comma* independent clause *comma?* *coordinating conjunction* independent clause

I have a sentence that starts with a dependent clause, followed by an independent clause and another independent clause, but I'm not sure if a comma would be required before the coordinating conjunction. Here's the sentence:

"After taking the bus to work for years, I finally had enough money to buy a car, and now I can finally go to work without waiting outside in the cold for the bus to arrive."

In that sentence, I added a comma before the coordinating conjunction "and" because the clause after that is independent. But since a dependent clause comes before the two independent clauses, should the comma be removed? Is there a rule that states this?