Ok, when you moved the anchor point of the layer to get your horizontal rotation you created problems if you try to get it to auto orient.
The standard way to get a layer to make a perfect one-dimensional rotation it to create a new Null (Layer>New>Null. Make the null 3D (checkbox). Then parent the “Rotating Layer” (your 2D layer here, although you must check the 3D box) to the Null, now move your “Rotating Layer” as far from the null as you want it to rotate, “P” reveals position, change the x, y, or z depending on which axis you want to rotate, only the x for you, methinks.
So now you rotate the Null’s Y rotation and you’ve got your perfect horizontal rotation.
But you still want to “always face forward”. You can do two things,
1) Add a camera and select your layer (the rotating one) Layer>Transform>Auto Orient>Orient Towards Camera. OK, the layer will always face the camera and you’re good, until… you move the camera.. go to 2).
2) We’ll add an expression to counter rotate the layer as it is rotated by the Null. Alt click the Orientation stopwatch for your layer, then paste in this expression:
[orientation[0],- thisComp.layer(“Null 1”).rotationY,orientation[2]]
That just tells the layer to subtract the Y rotation from its Y orientation. Now the layer will always “face forward” whether you have a camera or not, or even if you have a moving camera.