What kind of sentence structure is this: the next day, a family of pigs arrived, and they invited their friends with them.
why?

                       A complex sentence is made up of ONLY one independent clause and AT LEAST one dependent clause. (“After the storm [dependent clause], I went outside [independent clause].) The dependent clause(s) can appear either before or after the independent clause, depending on the sentence.  

                      A compound-complex sentence is made up of MORE THAN ONE independent clause and AT LEAST ONE dependent clause. (“After the storm [dependent clause], I went outside [independent clause] and I picked flowers [independent clause].)

  A compound-complex sentence is also known as Compound sentence. 

The next day, a family of pigs arrived, and they invited their friends with them. = Compound Sentence. 
 
                                                                                       ~Zєυѕ