We're looking to travel for 4 weeks next May/June and will spend 2 weeks in Scotland and 2 in Ireland. Does anyone have experience with/thoughts about renting a car in Scotland and keeping it for the entire trip? Any problems with taking a rental on the ferry and using it in Ireland even though it was rented in Scotland? We arrive in and depart from Glasgow.
Each car rental company will have different rules. Best to check on your car company of choice and email them for answers. What you are proposing means taking a ferry from Scotland to Ireland and back again. You will want to check on ferry prices vs airlines. Check to see if it will be quicker, easier and more cost efficient to do separate car rentals.
Standard advice would be as given by Michele either flying over (the hopper airline would be the restriction on baggage for the trip) or Rail and Sail.
As to car hire. There are a few companies who allow UK mainland to Isle of Ireland (and back) rentals. but you would have to go direct to the company not via an agency and inform them of your intentions. There will be an extra cost as you are insuring in 2 separate jurisdictions (3 actually including NI). Try Europecar, Budget, and Hertz. But as stated check the viability against using separate operators UK and IE.
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Two rules for Ireland, Take your time & bring a sense of humour