Need opinion on which you like better/if you have better name suggestions. Character is a 19th century female born in Ireland raised in America.
You could try resources like this: https://www.google.com/url?q=http://www.irish-genealogy-toolkit.com/Irish-first-names.html&sa=U&ved=0CBwQFjAAahUKEwiN7NCV87fHAhXJaz4KHcqpAlE&sig2=8Od5HXB5FbogPE0Yet1Jzg&usg=AFQjCNGkCSNnhbTMIHuUusQ6NlgY59Gx6Q
I voted for the second choice, Mollie. Though the first is a lovely name as well, I think there would need to be more specific reasons for her to be given a more unusual name, like that. On the other hand, I know at least one family of Irish emigrants to the U.S. that intentionally chose the most common American ones, like Tom and Mary, over more Irish-sounding ones, to fit in better. Depends on the character's background, I think, though you, as the author, are the one most familiar with that.