Vitamin E oil could be good -- or bad. Most of the cosmetic preparations of vit e oil are based on Vitamin E added to a carrier oil. The bad ones add it to mineral oil. You could add Vitamin E to your coconut oil, if you wanted.
The problem is that vitamin E is most commonly from unstable seed oils, so it must have added preservatives to keep it from going rancid. An example is wheat germ oil. Good stuff, but you can't keep it on the bathroom shelf for a month.
I believe in putting edible things on my skin when possible -- if I wouldn't ingest it orally, why would I want to absorb it topically? So, I use food grade oil.
People talk about the specifics of fatty acids in coconut oil being good for the skin. That is beyond me. All I know is that it works for me.
By the way, coconut oil may make eye makeup smear. Try using it as a night creme on your eyes and using a non-oily moisturizer on your eye area in the mornings.