Complex sentence: When Homer discovers that Santa's Little Helper has also eaten his cookie, which Homer had bought earlier, he wants to get rid of the dog, but Lisa convinces her parents to keep him and take him to an obedience school first.
Split into simpler sentences: When Homer discovers that Santa's Little Helper has also eaten his cookie, which Homer had bought earlier, he wants to get rid of the dog. However, Lisa convinces her parents to keep him and take him to an obedience school first.