If the home has a basement, then it is not a slab foundation.An Alaskan slab foundation has the home perched upon a single cement pad under which the tundra/ground can move by frost. Then we found out this works in other areas as well. If there is no mold in the basement, then that is good.
In the barn, you have a coule of choices. There are products which will remove mold (Home Depot sells one - I don't remember the name, however). Use a respirator if you do the work yourself. Sheetrock is a good medium in which for mold to grow. Cool moist temperatures and poor ventilation provide just what it needs. An alternative is to replace the sheetrock in the barn with another product, standards for barns being lower than for homes. Wood and plastic products will work. Even ugly old paneling sheets will work. You can sometimes find these for free from someone who is remodeling. Get a fan in there if it starts to come back.