If it's become a negative or hostile work environment where co-workers shy away or treat you like a second-class citizen because they are also afraid of being negatively labeled, that's a good reason for giving two weeks notice if you can.
And if I read you correctly, it sounds they are currently scheduling you only one day a week? If so, that's hardly even a job. You still want to give two weeks. And I'd recommend just giving a vague reason such as 'family events' or 'school only' and not letting them draw you into a conversation. Or, leaving written notice or an email, which is probably a good idea anyway.
The really difficult question is your friend whose mom is the manager. And I recommend measured honesty, giving an honest answer but not TMI (too much information). In theory, her mom could have coached up the other manager even though neither one is the boss of the other, but relatively few people have these skills, which work only some of the time anyway. Maybe just tell your friend this other manager was really impatient and it was a negative workplace, and leave it at that.
They're really expecting you to be like a NASCAR pit crew, fast, accurate, precise, and there's no way for that to develop overnight, and a good business person understands that.