There are a couple of different ways you can approach this. I am not sure which would be best so you might want to play around with them...
1. Use the LV ActiveX Server. This is an ActiveX object that you create in your C++ code and allows you to load up and run VIs, pass data back and forth, etc. The VIs are run in a seperate process from you.
2. Create a DLL instead of EXE from the LV VIs. This results in a C-style DLL that you can then call from C++ and obviously pass data back and forth. The VI's themselves are then run in the same process as the user's application.
BTW - I am not sure about what problem you mean about ALT-TAB...