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To find the range of a data set, we subtract the minimum value from the maximum value.
For Madlyn's family, the minimum value is 9 and the maximum value is 44. So the range of Madlyn's family is 44 - 9 = 35.
For Parker's family, the minimum value is 14 (from stem-and-leaf plot, key 1 | 4) and the maximum value is 52 (from stem-and-leaf plot, key 5 | 2). So the range of Parker's family is 52 - 14 = 38.
The difference in the ranges of the two data sets is 38 - 35 = 3.
Therefore, the difference in the ranges of the two data sets is 3. Answer: \boxed{3}.