Hello, Antonia
a single word denoting the thing in question can hardly be found. One precise match would be domestic altercation, which, however, is used in a legal context (especially in criminal law). Apart from that, you might find useful the following synonyms:
- war of words, high words - especially when the conflict is accompanied by shouting;
- wrangle, argy-bargy, squabble - conflict over trivia, something unimportant.
To make the reference to family relationships more explicit, just add family before these words.
Finally, generation gap stands for 'a lack of communication between one generation and another, esp.
between young people and their parents, brought about by differences of
tastes, values, outlook, etc.' This may also be helpful.
Respectfully, Gleb Chebrikoff.