What tools can I use for animating maps?
I have recently started using Google Earth Pro for Windows (free app).
It has the ability to export a recording, using the "Movie Maker" tool (under the tools menu). This will record your actions.
Strangely it cut off "Google Earth at the bottom right ("Google Ea"), I wasn't sure if this would cause them to complain about attribution.

I tried Google Earth with the Screen Recorder in PowerDirector, this works well and I am not limited by Google's speeds. (And the attribution was not clipped).

I find I fight with small things and can't quite get things just the way I want. However, it is free, and it does work.