Hi Lynne,
Tracing family history can be a challenge sometimes especially with records before 1864 as they were kept in the form of church and parish records, with all the surviving records having been sorted into county-based genealogical centres.
https://goo.gl/8N2tCDAs you mention, the early 1800's was a difficult time on the island of Ireland with the implementation of the Act of Union, the hated Penal Laws and the law of the land being administered from England. A tenant farmer as Micheal was, wouldn't have been a very profitable existence, especially with a large young family.
Most migrations around the 1840s were due to the famine but prior to that the prospect of a different life away from the increasing population of Ireland may still have been a pull to discover the America's.
Please feel free to share any images of the information you have as we love to see the records from back in the day.
Martin