You should look into PhantomJS (a headless WebKit browser), which comes with GhostDriver, which is the WebDriver protocol implementation for PhantomJS.
You will still need to use one of the WebDriver language bindings, which I'm not aware of any of the language bindings that are in C++, but perhaps one of the available languages could be used by your team for automation purposes.
Worst case, you could always create your WebDriver script in Python, and call the Python script from your C++ application.