'Straight Chillin', yeah right.

There is no real Hebrew equivalency for that term. if they said it, they'd say it in English. There are also plenty of Israeli teens that try and emulate 'gangsta/hip hop' cultutre too, just as there are plenty of Chinese guys that try and do it...and it's pretty goddamned funny.
If the kid doesn't know it's Hanukkah, then, that's the parents failing, not American culture erasing her identity. The Jews maintained their culture for 2000 years in nations that were devoutly Muslim and or Christian, what's stopping them from doing so in a modern secular state? It might also be mentioned that Christmas is still a big celebration in Israel as well.