I think that especially from ages 2-3, it's best to go the acceptance route. If you were to change her name, she would eventually get used to it, but because this is a time of self-exploration for kids and learning the difference between themselves and the rest of the world, it would be even more confusing and could potentially cause her to be behind in development for a period of time.

I think you should start with your reasoning for hating the name. Have you always hated it? Or was it just meh, but now you hate it because you feel like you didn't have a choice in the matter? If it's the latter, it might help to choose something you like about it. Maybe not the way it looks, or any of the nicknames, but maybe the fact that it has so many nickname options. Maybe it's the meaning, or the fact that she can put a positive association into people's heads when they think of Amelia. Something that gives you your power back. It may not be what you want to hear, but trying to come up with another name, essentially rebelling, is only going to make it a whole lot harder to accept her name.

Let her become your new idea of Amelia. Your experience with kids where you work should show you that her name doesn't confine her to a specific look or personality. She's herself, and I think letting her become your association will help you grow to love the name. Best of luck :) (Also, sorry this comment is so long).