The word "bicker" is synonymous with the act of arguing over trivial matters, to argue or disagree over small petty things. In this regard, it can be said that it has the same denotation with the word "fought" as used in the original sentence.
So, to make the change in the word "fought" giving it a more positive connotation but still retain the same general denotation, the new word is "bickered". This is because though bickering is a word used to refer to arguments or disputes, they are generally used in regard to small issues and not some big arguments. In other words, we can say "bickered" has a less violent/negative feel than the word "fought".
Argumentative and narrative are two different types of essays, argumentative tries to prove a point to the reader. Narrative essays usually tell a story through characters and dialogue.
