It's easy to say "man, if I was there I would have handled it like this", but racism makes people feel a type of way. Maybe the mom has experienced it herself, maybe she doesn't want that shit in her kids' lives considering all the horrible problems happening today, maybe it's both.
In retrospect, maybe she could have said less curse words, but you can remedy that by having a conversation with your children and being honest with them.
Like, that shit hurts you to the core, and to see your kids experience it is something I hope I never see.