You don't know the solar system is supposedly moving throughout the galaxy?
I do know that but I don’t know why you’d expect any solar system model to account for it. Because it makes no difference to the movements of the planets or moons in the solar system.
Why would you add unnecessary complication to a model when it isn’t needed?
Then why did this: 
get out?
I don’t know what you mean by “get out” but I assume that animation was done to explain to the layman the fact that the solar system is moving.
I am getting at providing an accurate CGI representation of a moving solar system, according to the scientists...you know, real "sciency," based on Newton/Kepler/Einstein math...
I don’t know if that exists, to be honest I’m not sure what anyone would do it for.
Maybe someone has but I’m not going to look for one. I’m not sure what you think it would prove. An accurate model of the solar system - and we have those - should give enough confidence in the laws of physics which underpin it.