Use two AnimationPlayer nodes.
The first one will be for the regular animation and the second one
will be used for the forward and back movement you wanted to do.
(flip only the first animation node using "
flip_h = true/false" if you only want the right to left movement).
As long as you dont have a position track on the first animationplayer, the second one should be able to do the movement you want flawlessly.