James Michael Kelley

I’m looking for information on my mom’s Irish family. Her great-grandfather was James Kelley (they may have called him mac or Mike). We have been told there’s a family bible that says James McMichael Kelley, but we have not seen this bible. What we know of our James is he was "most likely" born in 1828 and left Ireland between then (we are thinking late 1840's) and 1869 when he married his first wife in Tennessee, America, Nancy. His second wife’s tombstone says “wife of James Mc Kelley”. My mom, her brother, and my ancestry DNA says our family is from North Leitrim and/or Northeast Sligo. 
His first son was named Thos (b. 1869), and his Daughter Ludelia (b. 1876, d1947 )with his first wife Nancy (married 1869 b.1835, d1877). He also had a John (b. 1883 d.1966), James (b. 1882 d1959), Hurchell (b. 1886 d 1944), and a daughter, Mary (b.1879 d 1978) with his second wife, L Ellen (m. 1879 b1854, d1920).