Dave,
There are a couple of things you can try.
First, if you can build the external application as a DLL, you can call it from within LabVIEW to have it appear as you want. It doesn't sound like this will work though, but if it does, go with it.
Second, try hiding your LabVIEW window(s) programmatically.
Third, use the WINUtil.llb from NI's website to control the window appearance, to make the window for your external application (you will need the window name/handle) appear on top (be modal).
If these suggestions aren't appropriate, or do not work, please post some more detail on your situation, and try to provide a screen shot. Us LabVIEW programmers require visual aids before we can truly understand something...
-Mike