I am flying from Edinburgh to Dublin with a 12:50 arrival time. I then have a flight at 14:40 to Iceland. Changing terminals and need to claim bags. Also, an American traveling between these three countries. Have I allowed enough time?
If your plane arrives on time, or a bit early, you should be able to make it but it will be tight.
Any delay will make it harder.
Arrivals from the UK are going through passport check in Dublin, then you need to collect your luggage, exit go to your new terminal and drop your luggage for the next flight, go through security and make it to your gate.
Even if your flights use the same terminal you will not be much faster, as you will need to exit and re-enter to drop of your luggage.
If you have not yet bought your tickets, I would want much more time for the transfer, 3 hours minimum but 5 hours would not be too long in my view.
Better to buy your connecting tickets always from the one airline, first of all, they will not sell if the connection is too short. Secondly they will take care of your luggage when changing planes (and mostly they will use the same terminal) and thirdly, they will get you to your destination if your incoming flight is delayed.