You began the job in June, two months, you could have been travelling. Your MB is thoughtless and inconsiderate. Move on and do it quickly. Do not believe her when she tells you she will try to be on time in future because she wll not do so. She, obviously, has no respect for you or she would treat you better. You are "the help," and nothing more.

MB here. This is not ok and is incredibly poor behavior on the part of the employers. I'm sorry OP.

Definitely start looking for another position - given how short this tenure could possibly be I think you could honestly explain to a potential employer that this wasn't a good fit and you're moving on as soon as you realized it.

If they press you can explain that your 11 hour work day routinely was stretching to 12 hours without warning or notice and that level of fluctuation was difficult for you. I would certainly understand that.

In the meantime though, it might be worth another conversation with your employers. Perhaps you could tell them that you love their kids and really want this position to work but you can't be as flexible as they seem to need. If they seem to regularly need 12 hours of coverage, and if you're willing to consider that, then they and you both need to adjust expecatations and compensation. If they can't/won't do that then you have given them more than fair notice about this being problematic for you.

I think this is enough outside reasonable behavior and expectations that even if you pay the price with a recommendation, future employers (with a brain) will understand if you tell them what happened. I certainly would.

Sorry! Good luck finding something better.