How do you get rid of calcium build up in the water of a Travel trailer used only 4 to 5 times a year?

We love to go to the desert dirt-biking during the winter. But we seem to have a recurrent problem of calcium building up in trailer water lines causing headaches more often than not. It clogs up the toilet inlet and even the cold water spout. Our friends told us to use a filter which we have been using for more than a year but continue to have the problem. Please note we were unable to get any of the cold spouts to work at all this weekend but the hot water worked fine. When we got home and pulled the lines, there was a good teaspoon full of calcium in each of the lines totally gumming up the lines and the Trailer is only one year old. Please note we do use this to drink, cook, and wash, so running CLR through the lines I don't think is an option. Short of getting a water softener for the trailer I really need some help. How do I keep this from happening?