Odd head turn help for 2d animation.

Question

I've been following online tutorials from lynda.com and I'm very new to AE. I wanted to animate my characters from my webcomic (Maybe NSFW) http://sotsog.net/archive/23-necronomicon/ and after reading up and experimenting with Flash it turns out AE would be a better fit.
The tutorials I'm following are incredibly helpful but the character used in the demonstration has some different replacement animations as well as a completely different mouth. For my characters the mouth is always at a side view and I don't mind a small blink or hole in the animation when going left to right but this has lead to some issues.
I'm at the point in the tutorials where I'm creating a master control where my head will continue to turn on the slider and allow me to easily change the mouths. Through the course I've already set up rotating head/eyes/mouth. At this point I'm removing each part that will use some sort of replacement animation from my "head" comp and putting them into a master control. So my blinks/mouth/head rotation should all be set in there. In the example the demo character's mouth moves from left to right in a fluid motion and used an expression with:
a=thisComplayer("head").timeRemap;
b=timeToFrames(a);
b*13.5.
This was for just moving the x-axis. Because my character is "flat" im not worried about y axis or scale at the moment.
My mouth does not move at a constand rate like the example.
Here I am at frame 0
Frame 10
Frame 20
On Frame 10 and 20 they are kinda in the same spot. my x/y positions read
146.5, 165.0
105.5, 167.7
102.5, 167.5
Again I'm not worried about the y axis
As you can see its not as simple as from left to right and i need three points in my expressions equation. I think the best way to describe it is frames 0-10 will have movement. I will have the animation expression linked to my head turn time remap so it just keeps turning although I would like it to stay stagnant at frames 10-20.
Now to make matters worse I would also like to flip/or reflect my mouth between frames 1 and 10. Hopefully since they are already all within the mouth comp all my replacement mouths for animation will also be flipped when the head is turned in that manner. If I can set up an animation expression on frame 3 to flip i think that would work out but again im having trouble finding the right formula. Also I'm sure I'll need to change my keyframe interpulation to Hold in that instance as well so it just quickly jumps to the reflected mouth.
The course I'm taking does not cover this and I'm having trouble finding a solution through search engines. Any help would be much appreciated.

Answer 1

I may have worded this weird. My hierachy does not seem to be an issue, I have my entire character rigged aside from this one complication. I've been flipping my mouth in my mouth comp by unlinking my scale and putting it into the negatives with a hold on my keyframe interpulation. I seem to have fixed that issue but now im just trying to get this mouth comp to follow my head turn. I've linked my mouth comp to the heads timeremap so I get those 20 frames of movement. I just want it to stay still for a few of them. Are you sure theres no way to set an absolute number or once i hit frame x to stop x-axis animation?  My frames 0-10 of x-axis movement works just fine and at the speed I like with.
b=timeToFrames(a);
b*4.
I placed my mouths where I would like them positioned on my time line and recorded for frames 0, 10, and 20. These read 146.5, 105.5, 105.5. (this is only x-axis and unlike my original post I'm just going to leave frame 20 the same as frame 10. frame 20 was originally 102.5 in my first post but thats a very slight movement thats unessesary.)
Now I just need it to stay still between frames 10-20. I would think this could only be solved in my expressions. I just can't figure out a forumla that would work.
Thank you for the link but this did not solve my issue.