How do I change an objects graphic sheets?

I'd like to have an object use a sequence of images when going in one direction, for animation and when going in another direction use another sequence of images.

I could technically have all the images in the same sprite object and carefully control when the frames show, but it seems a bit of a hassle. Having two sprite objects and destroying one and replacing it with the other seems a bit convoluted. Is there another way?

Why can't you just make MovingLeft and MovingRight animations and switch between them depending on the state of the sprite? Maybe I'm misunderstanding what you are wanting to do.

I'd like to use constructs regular animation system to do the animation. The sprite (a cart) has two images for moving left and constructs regular animation system is good for that. If I put four images into the sprite (two for moving left and two for moving right), I'd have to turn off constructs animation and start manually programming frame changes.

Just make 2 animations.

Play them when needed.

In your case, duplicate the animation, give it a different name, delete the frames that in each are not needed.