You can use theVI server to open a reference to the other process (I`m assuming that both processes are LabVIEW processes). If the program is in memory, the name of the VI should suffice (Path is not necessary).
Then you can poll the property "Execution.Status" to see if the target process is running or stopped. Linking this to a comparison or case-structure (The Enum makes the case structure perhaps easier to read) you can programatically stop the second process as soon as the first is no longer running.
Shane.
Using LV 6.1 and 8.2.1 on W2k (SP4) and WXP (SP2)