This is one of the more curious Spanish expressions to me. I think it was first introduced to me by my Spanish friends in England when my future wife traveled alone to Spain for a wedding and I had to stay behind because the British immigration officers were getting uneasy with me going to and from Spain so much. Here’s a brief definition of the expression, followed by a longer explanation I’ve gathered from some internet research:
estar de Rodríguez: adj. the state of being left at home alone to work by one’s spouse (wife, typically) and children, while they go on vacation.