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.
The phrase originated in Madrid in the 1960's and 1970's, at the end of Franco's dictatorship. During this era of Spanish history, there was a huge divide between the sexes in terms of social responsibilities and rights. A woman, for instance, could not open a bank account without her husband's or father's signature. Men were the primary breadwinners of the household and were considered completely inept with household chores. Women stayed at home raising the children, buying groceries, cooking and cleaning.
During these two decades, jobs were scarce, and it was very common – the norm, even – for families to leave the small agricultural countryside towns to go live in a big city, where the man could work a blue collar factory job. As a result, almost everyone in Spain has a hometown, referred to as el pueblo, that they are originally from, and many people still retain a house there. What the Spaniards I've met most often do with their vacation time is go back to their hometown. Thus, there are little dormant towns dotted across Spain, consisting of empty houses and a handful of year-round residents, that burst to life with emigrated residents during certain festive times of the year, such as Easter, all of August, and All Saints Day, a day when most Spaniards go visit their relatives' graves. As will all traditions like this, eventually this ebb and flow of Spaniards to the countryside will cease, as younger generations feel less connection with their parents' and grandparents' hometowns, but it still has another generation or two of life in it.
Back when women were primarily housewives, it was common for the women to take the children (via bus or train, I suppose, since few women of that era ever learned to drive) back to the hometown a little early, before her husband got off work for vacation, and return later. Thus there were these times on the edge of vacations when the man would be home alone, left to fend for himself with whatever cooking abilities he possessed. And that is what it means to be de Rodríguez.
There is a sense of playfulness to it, as in, "The wife's gone, so I'm free to go out and party with my bachelor buddies!" The most equivalent English proverb is, "When the cat is away, the mice will play!" Personally, I use it as a time to leave empty beer cans around the house and then spend the last day cleaning the place up so all is spick and span when the cat my lovely wife gets home.
As women gain more and more equality in Spain, and men take more household and childrearing responsibilities, this phrase is also beginning to be apt for women to use as well.
The most frustrating aspect of this idiom is that nobody seems to know why the surname Rodríguez was chosen. It's one of the most popular surnames in Spain. I'd like to think that it originates from one particular neighborhood in Madrid, where some fellow's wife and children left him and he went wild with his freedom. So all the other men, when left temporarily by their families, would joke that "I'm like Rodríguez [for a few days]", referring to that one individual.
This morning, my wife and daughter left to go to my wife's parents' hometown for a few days for Easter and left me home to work. ¡Estoy de Rodríguez!