with whom do you want to go to the skating rink?

С кем вы хотите пойти на каток?

Ответ: I want to go to the skatingring with my family. I hope we'll have nice day!

With whom do you want to go to the skating-rink?

 I want to go to the skating-rink with my friends. 

С кем вы хотите пойти на каток?

Я хочу пойти на каток со своими друзьями.