Ok. Sorry. I didn't know the rotator did a distortion as part of its rotation. If you feed a rotation into a distortion, it does a flattened rotation, like what I was experiencing. If you feed a reproportioned UV into the rotator, it skews the image like what I was looking for. 

Would it be possible to add a note that it does that distortion to the rotator descriptors in the Nodes section?

The more I mess with this, the less likely I think it is. 
You need a way to multiply the values based upon their facing. When the UVs are flat, you multiply them by a flat value, as they get closer to 45 degree angles, you multiply by a gradient, but the gradient needs to be facing complementary to the existing gradient.

Soo... Yeah. Anyone know another way, because I don't know how to do that.

I'm still trying to think through the problem, but here is the demonstration. 

Little correction, when I say yellow opposes yellow, I meant red. I do realize the yellow is the combination of green and red.

Also, there may be some way of doing this using UV tricks, so if anyone knows, I'd love to hear it. I think maybe a multiply with a stationary against the rotating may work.. not sure. 
Although, even if that were to work, I'm wondering if there would be harm in allowing this change? I can think of ways around it, but if allowing vector4 wouldn't cause performance hits, it would make this process easier to setup. One could chain texture_2Ds along with UV distortion for very complex behaviors.

I want a Vector 4 instead of the texture input, not instead of UV.
Right now the input on a texture_2d input is locked to only connect to a texture output from texture_asset. If it accepted a vector4 (rgba), I could apply a uv to an image, output that image into another texture_2d node and then apply a separate UV. 

I'm in the process of uploading a video to show the issue. 
To get an idea of the effect I'm trying, see this hearthstone image, Healing touch. It has two rotating but distorted disks. If you can demonstrate out how to make that effect, please let me know.

I tried this, and it doesn't work.
Picture two identical 0 to 1 gradients. If you rotate one 180 and add them together, you get a solid 1 value. 
So, when I attempt this add method, because I'm adding to gradients that are rotating in and out of 180, the object distorts wider and skinnier repeatedly. 

There is no distortion I can do to a rotating gradient by using other gradients to reach the effect I'm looking for. I need to distill that information into an image and then create a new UV distortion over top. If texture_2d allowed vector4 instead of a specific texture input, I could feed the rotating image into the vector4 input and then a new UV to distort it. 

Looking at documentation, I fear that maybe the writer was getting the texcoord thing confused. I'm hopeful that someone can figure out how to get more UV sets in, though. Even if it means grabbing them from a copies of the model 2 UV sets at a time.

Please please bump this up a priority level. Even on a high resolution monitor the screen if filled in seconds. It's not necessary to make new shaders, but good navigation makes work times faster.
PS. Consider adding bookmark jump to locations. And area blocks with commenting. The program is fantastic, but when a shader gets complex, some quick jump to points and some area blocks to organize and document would help a lot.
Example: Your leaf texture is fairly large. If there was block commenting, it could have the section that does the wind deformation labeled, and it would be easier for new viewers to understand. If I were in a production environment, I could hand that shader to another employee. They could jump to the wind section and tweak behavior with less deciphering.