Since the problem only asks for the difference in the $ x $-coordinates, we can ignore the $ y $-coordinates. They originally agreed to meet at the midpoint of $ (3,5) $ and $ (-6,2) $, so the $ x $-coordinate of the planned location is $ \frac{3+(-6)}{2}=-\frac{3}{2} $. The correct meeting location should be at the midpoint of $ (3,5) $ and $ (-10,4) $, so the $ x $-coordinate should be at $ \frac{3+(-10)}{2}=-\frac{7}{2} $. The positive difference is $ -\frac{3}{2}-(-\frac{7}{2})=\boxed{2} $. Alternatively, notice that a 4-unit change in the $ x $-coordinate of Barbara's location resulted in a 2-unit change in the midpoint since the 4 gets divided by 2. $ \frac{3+(-10)}{2}=\frac{3+(-6)}{2}+\frac{-4}{2}=-\frac{3}{2}-\boxed{2} $.