guess there would ne no reason that Jenny and her kids couldn't stay at the Winchester's old house, although I'm not sure I would want to

I wouldn't want to, either!

I always thought that she would have stayed.

She probably did. And I've watched that episode a million times and don't know why I thought about her leaving only now. :-)

I absolutely love the scene when Dean finds Sam upstairs with the lamp cord around his neck. And that little hug

Yes! Big brother to the rescue!