I know this is a complete stab in the dark, but I have a relative named Elizabeth Eagan who was married and lived in Mineral Point, Wisconsin in Iowa County. By the Irish naming patterns of her children, her mother's name could have been Margaret. She married Francis Mullen. in 1850 so we believe she was born around 1830. The census indicates she says she's from Cork and immigrated through New York. Does that ring a bell at all?