It seems both the avatar-control-center and avatar-remote-deployment-unit prototypes are mis-defined. As you include a pictures field, but this isn't valid for a car type prototype. The sub values of your pictures should be in the animation field.
https://github.com/DedlySpyder/Avatars/blob/master/prototypes/entities/enterable-entities.lua#L33
https://wiki.factorio.com/Prototype/Car#animation

As in my quick test the control center's radar dish on top never spins, despite you having made the 64 rotations for it in the graphics file.

despite you having made the 64 rotations

Stole from the old radar spritesheet actually. My assumption was it doesn't spin because the player doesn't actually rotate the car, so even fixing the format probably won't fix the animation.

One day I might rework the entities to be composite. Layering a power consuming entity that has normal animations to spin the dish with a hidden car on the same spot. Then I could disable/enable the car based on powered state. Thats just the base idea I've always had, never really put a ton of thought into it.

Vehicles have animations for when they are moving, so I guess it would only spin when the vehicle is moving... Yea I might have not quite thought that one through fully.

I only noticed it as it conflicted with a mod of mine, but that was on my code error/gap :)