I must be missing something. Normally I get that effect by drawing the first dimension string, dragging a copy, and inserting (command-clicking) or deleting points for the new string. While the two strings are not related to each other, both are related to the same points (which is the foolproof cool thing about dragging the copy).
What would the parent-child relationship add to that?
[only thing I can think of after typing the above, which is not minor: fixed distance between dimension strings, so that you drag one and the several related dimension strings move together)