I'm a little confused by what you are trying to accomplish here, so forgive me if my suggestion is completely off. However, if I understand you correctly, and what you are trying to do is what I believe you are trying to do, I managed to do it in a couple seconds.
- copy/paste (or just drag over whilst both files open) the eyes only layer of picture2.psd back into picture1.psd of the cat. Then reduce the opacity - although this isn't necessary here, it helps a little - of the eye layer and move it into position with the 'move' tool, or whatever that tool is called on the top right of the tool bar. Once you have it close enough, doesn't have to be perfect at this point, then hit Ctrl+T to bring up the bounding boxes of the tranform tool. However, don't move it by hand, but instead, move the contents of the layer - the cats' eyes - by using the arrows on your keyboard. Furthermore, it's best not to click inside the bounding box to apply the tranformation since you might accidently shift it out of position - we've all done it. Instead, click on the move tool in the toolbar again and you'll get the same dialogue box, ie. apply the tranformation? click apply. Once it's in place, or you 'believe' it is, then put that layers' opacity back to 100%, and then turn the layer on and off to see if you've really got it in place. If the picture jumps or jerks around as you tun the top layer on and off, then it's not in place and you'll need to repeat the steps of hitting Ctl+T, and shift it over with the arrow keys until nothing jumps around, then it is in perfect place.
(I don't know how this could be done, however, if the two files were not the same ratio, that would be a huge problem.)
- now, you said you'd like to remove every instance of the eyes layer from the picture of the whole cat. Since the two are in perfect position, and I do believe every pixel is in exact position, then you can do whatever you want since you now have source for a selection (the top layer in this case) to manipulate the underlying layer of the cat. Ctrl+click the top layer (in this case) and then do whatever you want with the layer of the whole cat.
It's kind of like going backwards I guess. I'm curious, what's the reason you want to do this?