The short answer here is you can't! At least not like this. When you call stop() at a particular frame in the timeline in a movieclip, it stops playback at that frame for all layers in that movieclip.
But if you put the frames for the animation in layer 2 into a separate movieclip and then drag the instance of the movieclip onto the stage in layer 2.
So layer 1 contains whatever you currently have and layer 2 now has a child movieclip containing your other animation; then where you've put a stop in layer 1 of the parent clip, the parent clip will stop playing. But the child movie-clip on layer 2 should continue playing as it has it's own separate timeline.
Not sure if I've explained this well enough, but it's kinda difficult to explain clearly!
Hopefully the attached image should help to explain things a bit better....
I've used frame 6 as a stopping point, just to space things out a bit in the image to give you an idea of what I mean.
In the child movie clip you create you might want to add explicit calls to play() and stop() at the start and end frames of the animation, to ensure that it plays and also to ensure it stops when finished. (unless you want it to repeat indefinitely, in which case you can omit the call to stop() at the end!)