Do I need a comma between two independent clauses in a series?
I bought a CD and a book.
But what if the two items in a series are independent clauses, in which case a comma would normally be required, for example,
Remember that the 30th is a Sunday and we are closed on Sunday.
In a way, this does seem like a compound sentence which would require a comma, Certainly a comma would be required if the sentence were
The 30th is a Sunday, and we are closed on Sunday.
But with "Remember that..." it seems as if this is no longer a compound sentence but rather a single independent clause with two elements in a series (which are themselves independent clauses). Therefore, my question is whether a comma is still required before the conjunction.
Any help from fellow grammarians would be appreciated, but please don't advise that I rewrite the sentence, as people often do when answering grammar questions they don't know the answer to. I want to know what is correct in this situation.