So, as to your first question. I admit it's a bit tricky… but what you have to do here really is not TALK about leadership but SHOW it through PROOF! Meaning through concrete actions and results!
As for your second question… the story as you tell it, seems a bit trivial.. the whole details about bringing the children or not, is not really that important.. what IS important is your relationship with your firm, and with the client.. and how you dealt with the challenges inherent in the story, and most importantly, what CONCRETE results came from it!