Planning the above trip for late April, 2016. What is best way to get to Shannon Airport from Seattle, WA., Or to from Sea to Dublin and from there to Ennis, Ire.? Trip begins in Ennis and ends in Dublin.
When I did the longer RS Ireland trip in 2014 I flew SEA -> AMS -> Dublin. That worked fine for us as Aer Lingus had a number of flights from AMS to DUB. I like to do the overseas leg from SEA (or SLC) if I can and change planes in Europe instead of having to hassle with changing on the US East Coast. I do not know what kind of connections you might get from Amsterdam to Shannon.
You can look at one of the sites like Kayak or GoogleFlights (used to be Matrix) and see what comes up, then book directly with the airline.
Go to Kayak Flights: http://www.kayak.com/flights. Choose "Multi City" on the top. Put in Seattle to Shannon as the first leg, and Dublin to Seattle as the second leg. Check "Include Nearby" to get other close airports. Make sure you have the right dates; particularly from the West Coast, flights to Europe are not always daily.
See what comes up, in terms of flights and costs. Next, you can use the filters on the left of the page to choose connection airports, airlines, layover times, etc.
From Seattle, it saves a lot of time if you go to Europe nonstop, then connect to your final destination. It's also better if there's a problem; from (say) London to Dublin there will be multiple flights a day, whereas from New York to Dublin there will be fewer options if your arriving flight from Seattle to New York is late.
If flying out of Vancouver is an option, look for flights from there as well; this may give your more options and/or lower fares. Only you can decide if the extra driving time to get there is worth it.
We're doing this tour in June. This may not be the cheapest option, but we're going non-stop SEA to LHR. We got a fare sale, so we've already booked that piece. I suspect we'll grab another flight to Shannon the day we arrive. We are headed to a conference in Glasgow after the tour, so eventually we'll get ourselves back to London either by flying or taking the train. I'm sure others chime in with options.
We flew from Vancouver, BC this past summer to Dublin (changing planes in Toronto). Even factoring in a night at a hotel there (and dinner, etc), we still saved quite a bit of money. The Canadian dollar is weaker than the American dollar, so that helped. We drove up from Seattle and found the whole experience very fun and worthwhile.