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I looked at transcriptions for the 1868 and 1882 civil death records for the two Andrew Mulvees. The 1882 record is very likely for your great-great-great grandfather. The 1868 record was for an Andrew Mulvee who died in the Ballinasloe workhouse. I'm inclined to say that the 1868 Andrew was not the father of the 1882 Andrew. Unless there was a falling out between the two, I don't think the older Andrew would have been in the workhouse if his son had a farm. They may be related but more work would be needed to confirm.