I don't think you need "about" in this sentence. Just "discussing our family tree" is fine ("about" makes it sound a little awkward).

Also, what does "choisir un arbre généalogique" mean exactly in French? Is it still discussing, or choosing?

Okay, it seemed that it was not the only error >.<
I've changed this IRC delirium into the suggestion of saeb, so please check :)

I think 'drawing together' is ambiguous in meaning. With what sense is it used here?

with a pencil and a sheet of paper XD

I like CK's suggestion.

Well I put the CK's version, and I think the other sentences are quite OK, but I need the confirmation of a native/advanced speaker of both French and English (like FeuDRenais, Scott or Trang) :)

For the record, I am not a native French speaker (not even close...)

And barely, barely advanced...

Btw, I would put "together" at the end of the sentence, since I think you're emphasizing that they drew the tree together, and not that they spent time together (which they obviously did, since they drew the tree together).

LOL I leave you do everything you want x)

(p.s. we really did that...)

Okay, I changed it a bit... I don't know about the Italian, so correct it if you don't like the new version. But I think it's more or less in tune with the French.

I think it's very good now^^ thank you very much :) :)