I started a thread a long time ago wondering about the meaning of this song. Sorry, I'm not a blue clicky thing guy or I'd link to it.
I was talking to my uncle about it a few weeks ago and he thinks that Rose Connelly was a peasant girl put in "the family way' by the narrator of the song, who would have been of a higher social status, perhaps even an English land owner in Ireland, Rose being native Irish. The father basically says to get rid of the "problem" if he wishes to not be driven from the family and it's fortune, of course the mistake was in getting caught. Apparently there are many songs based on this theme.