Edit: the answer to your edited question is unambiguously “yes, we are”. Short answers use the same auxiliary as the question:
- Are you doing fine? — Yes, we are.
- Do you want some more tea? — Yes, I do.
- Will you marry me? — Yes, I will.
- Can I go to the swimming pool, daddy? — No, you can't.
It's not exactly clear what you are uncertain about, so I'll try and do my best. There is nothing specific to “having a good time in this question”. To the question “Are you playing with LEGO?”, the kids might answer “Yes, we are” (akin to your choice #1) or “Yes, with the big castle” (somewhat closer to #2), or plenty of other things. All are legitimate answers, as are the ones you propose in your question.