Hi Collin,
I've attached a QLab workspace with a couple solutions to this.
The first one (cue 1 to start, cue 2 to stop) assumes you want to wait for completion of the current sound in the random group before triggering another one.
The second one (cue 3 to start, cue 4 to stop) assumes you want to trigger a new random child based on a specific time wait (in this case 4 seconds - the sum of the post wait on the random group and the pre wait on the start cue to restart it)
Both will let the current sound in the loop play out when the loop is stopped.
Hopefully one of those does what you are looking for?
-Arshan