A simple solution is to use a rendering-request mechanism, as implemented in CTK’s render window - used in applications such as 3D Slicer and MITK. In 3D Slicer we use this for real-time rendering stereo virtual reality display and it works fine.
renderWindow->Render() is all you need. When that call returns, the rendering is already completed.
The error in the code snippet is that you set the same input into vtkImageAppend every time. Instead, you would need to make a deep-copy of the vtkWindowToImageFilter output and set those as inputs into vtkImageAppend. But instead of this of course it would be much better to render the scene directly to your display in real-time.