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Train roundtrip from Dublin to Portrush

We will be traveling from Dublin airport to Portrush in July 2019 for The Open. Will need to get from Dublin airport to Portrush train station and back one week later. I understand there are 2 rail lines and was advised best to get to Belfast first on one train line and then get a different ticket on another train line from Belfast to Portrush. Suggestion appreciated on this. Should we/can we do roundtrip? Get tickets at the station on day of travel? Thank you~