Shortening of names can lead to much confusion. My youngest daughter's name is Riyadh. At home she's known as Addie, although when she was younger (and still sometimes) I call her Libby (long story, favourite book when she was small).
As a result, one of my workmates thought I had three separate daughters: one called Riyadh, one called Addie and one called Libby. As I do have three daughters, but the other two are Vienna and Fern, this caused much confusion when they met my children.
I also know an Evangeline who is always always known as Evie.
So Emmeline being shortened to, and known as, Emily, would be perfectly common, just confusing when both forms of her name are used. We should agree on one and stick to it!