Honestly OP, being a nanny in the U.S. is super difficult (not even because of the kids but the parents) and is VERY low paying. I would find another dream if I were you. (I’ve nannied for over 10 families in 3 diff parts of the country).

Don’t let your Boss threaten you. Now that he knows you’re interested in leaving the company I’m sure he’s in process of finding a replacement for you. You just gave him another month to do so. Then you’ll be fired instantly. For whatever reason. Actually Bosses don’t need a reason to let you go instantly most times. If he gives you a bad reference then he needs written documents. Otherwise you can take him to court under slander/liable charges. Nannies don’t get paid that much. That’s because, oftentimes, they don’t have to be. You’ll live there free. And eat the same food they do. Also free. Sometimes even use the family car for free. See if you can catch a couple episodes of “The Brady Bunch”. So, given that, you don’t need to be paid very well. And you’ll also get a taste of being a Mother to these kids. Good Luck.

I don’t know about where you live but in the U.S. you can threaten to sue him.

Report him to HR, or file harassment charges. You gave him more than a required two weeks' notice and he can't force you to continue working for him. He has a boss somewhere and you have the law on your team. Live your dream.