Unless someone from the family answer your post the only option I think you have is parish records.
In 1856 Galway there were 104 Dillon's and in 1857 Mayo there were 116 Hart's.
Both counties belong to an Irish History Foundation which has baptism and marriage records depending on the existance of parish records. You can search for a small fee with a year and name and county. If you find one that seems to fit you can then purchase a baptism record. A baptism record has
mother and father's names and mother's maiden name, place and parish. Once you have a father and mother for Michael you can then search for the siblings.