Thanks to all of you who wrote.
Since we have two cars and a car-sitting solution can only apply to one of them in my circumstances, the least harmfull option for the other car is going to be to drive it to the airport and then park it long term for $10. This way the cost for 7 days will be about the same I would pay for 2 fines and transportation to and fro the airport for 4 of us, while making the trip much more convenient. Unfortunately there are no locations in this area that are only illigal to park in one day a week, that I know of.
Amos