Leaving disrupts the dinner for the offending table, not the rest of the diners. Nobody would notice if she just left without causing a scene. People leave restaurants all the time. Those are the people that matter and those innocent third party diners are people whose feelings should also be considered when deciding what the best way to deal with a situation is. OP’s family deserves to be embarrassed because they behaved in an embarrassing way, but the other diners did nothing to deserve having their evenings disrupted. That’s why it is the best option.

And it seems it was an option, because OP said she got up from the table and shouted at him and describes some of the things they said about her “after she walked out.” That would suggest that she did get up and leave, but chose to shout at her family instead of say what she needed to say at a volume that didn’t disrupt innocent third parties.