The way to do this is with the VI Server. From one.vi get a reference to second.vi and launch it using the Run method. Then have one.vi close itself by getting a reference to itself and closing its front panel. Note that your code should also be written such that one.vi stops executing once that occurs otherwise it will keep running even though the front panel is closed. So, if you have some sort of while loop that continuously runs you will need to stop it.
