It's standard procedure in business to have a written job description, so both the employer and the employee know what is expected. Do you have one? If you don't, you need to ask for one, so you'll know whether she expects you to, say, do family laundry once in a while and can decide whether that's something you want to agree to. In your kind of job, you should also be able to expect notice of what you need to do each day so that you'll be prepared. It takes organization on the boss's part, but that's what a good employer does.
Perhaps your boss is under a lot of stress right now and not thinking ahead. But you can see how that stress affected you and even the children. You've been working for this woman only six weeks and that's not necessarily long enough to be able to jump in and take charge at a moment's notice.
Although you sound like a person who would be willing to go an extra mile in an emergency, the communication lines must always be working.
Can you talk to her and ask her to work all this out with you? If she says she can't, or is too busy, or gets angry, then you may have to choose between keeping a job with a substandard employer or trying to look for another place to work.
(Just read the other responses. Yes, check out the legality of the whole arrangement to protect yourself!)