That certainly is strange MamaBear.  I've drawn and painted pictures of people I didn't recognize.  One was a pretty bizarre experience that I've never been too comfortable with.  I painted a portrait several years back of a woman in old fashioned clothing.  It is hard to explain, but while doing it, I had this weird, compelling urge to get it done -- the type of thing where I was working for hours on it.  I've never been one to have obsessive behaviors, so this was really out of the ordinary for me.  Anyway, after I finished her, I was physically and mentally exhausted, and just sat in the floor and cried.  It was the weirdest thing!  I've never told that story.
After keeping the old girl around a few days, I decided to paint over her, but the face was very similar to the one before, maybe not quite as spooky.  I don't know if "someone" was trying to get some recognition, or what it was, but I am happy to say it hasn't happened since, at least not on that level.
The picture does give off a bit of a funny vibe.  I got the impression this might have been an older child, maybe a teenager?  Just curious, have your girls ever been kept by a sitter?  I just wonder if this could be stemming from a bad experience.  (I always look for the logical things first).  That certainly was an odd reaction from a child that young.