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I searched on the subscription site Roots Ireland and although they had a number of Dougher baptismal records in Mayo in the 1840s, none of the records had a father Frank or Francis. Likely they were baptized in a parish that no longer has records back to 1840. I also did not find a Frank Dougher marriage record.
I did look at the 1855 Griffiths Valuation head of household listings to get a sense where the surname Dougher (and varints) was found. Primarily, they were in North Central Mayo where in fact many families emigrated to Pennsylvania.
You may want to add your ancestor stories to our XO Chronicles site and possibly someone will see a connection.
Have you considered DNA testing?