First, download and install the latest GPU drivers for both GPUs. If it will help, you're lucky: I had something very similar on machine (dual GPU Intel + NVidia as well), and was unable to find a fix.
My advice - upgrade to Windows 8, install visual studio 2012, and WP8 SDK. Fortunately, with the recent version of the SDK you can still build for the previous WP 7.1 platform. And even if xde.exe still won't work on your laptop, you can test and debug the application you're building on new HyperV-based WP8 emulators.