Without seeing her or knowing the breed I am inclined to guess that she is a Mediterranean breed. Almost all Mediterranean breeds (except buttercups) have huge single combs and while the roosters' are supposed to stand up, the hens' combs are supposed to flop over to one side.
So, tell us what breed she is.
You can dub any comb. Cock fighters dub their cocks' combs so they don't get grabbed and torn in a fight. They make a special shears for the job.
If you live where it gets hot, I wouldn't trim it much because that helps keep them cool. It works like a radiator because there are so many blood vessels near the surface.
I've raised Minorcas, Anconas, nearly 1000 each Leghorn and Penedesencas. I don't consider those big floppy combs ugly at all.
Beauty is in the eye of the beholder.
And I believe they can see just fine. It is a lot better than those big feather crests Silkies, Houdans and Polish have.
If your hen doesn't like the comb flopped over her eye, she joins that opinion of millions of hens of the same breed that have existed over the course of hundreds of years.