Did you guys sign a contract outlining what is actually required for you to do? Sounds to me that your employer is taking advantage of you, or there was some king of a miscommunication between the two of you as to what is really required in this job.
If I were you, I would sit down and talk about it with your employer about your job. That is of course after you go over your contract, if there was any. From what you describe, you are doing way beyond what is required in an "usual" baby sitting job. It’s as though you are being treated as a live in nanny PLUS a house cleaner.
If after talking with your boss, it’s not what you want to do, I would quit and look for another job.
こちらでナニーというと、Care Giver と呼ばれる人たちで、契約によるとは思いますが、たいていの場合、子供の面倒を雇い主の自宅でみていて、Daycareに連れて行ったり、公園へつれていったり、自宅では、いろんなアクティビティーをしたり。ですから、幼児保育資格を持っている人が多いと思います。自宅で雇われている保育士のようなものですから、ベテランのナニーさんだと、自給$30とか、ほんとにしますよね。