bicker

We have learned smart words about argument: 1) contentious - causing argument. 2) altercation - noisy argument in public.  Here is another one:

bicker

verb.  argue over petty, trivial, unimportant things 

"Jeb Bush and Donald Trump bickered again at the GOP debate. Bush: You're never going to be President of the United States by insulting your way to presidency."

"The governments have bickered and quarreled, failing to agree on coherent policies."

"My two sons are bickering over who should use the bathroom first every morning."