So, this IS different from the Hana Yori Dango Final Special. You can find this one by searching "Hana Yori Dango 2 Special."
This is kind of a prequel to season two, but it's more like a game show type thing than a drama episode. It has Makino's family following her to New York and eventually they meet up with the F4 guys. It shows fun, cheap things to do in New York and also has the characters do little challenges. Cute and fun to watch, but definitely not essential to the Hana Yori Dango story. ^_^