I've read your Question 3 times, this is what I get...
1. You want to keep the Main Vi open until you tell it to close.
2. You need to keep the subvi open and running until the main closes.
These 2 modes will happen if your subvi VI Node Setup (rt-click on subvi to set) is set to "Open front panel when loaded" and "Show front panel when called"; leave the "Close afterwards..." unchecked.
Also, when you close the main, all its subvis will close automaticllay. But, on your subvi, if it contains its own while loop (which is good), make sure it won't close after just 1 run. In fact, you could create a node input that will set your subvi loop run/stop node based on a condition from your main VI.
Good luck with it, Doug