Can you not just say that you had to take a leave of absence from your previous job to deal with a family emergency? I believe if someone asked me why I left my old job that is what I would say. Something to the effect of...well I had a to take a leave of absence to deal with a family emergency and by the time I dealt with it, they had hired someone else. Or something to that effect. If they asked for more info, I would just say...oh the emergency is dealt with and all is well now. None of their business.
THAT particular emergency has been dealt with!
