Maybe I'll get kicked off the forum for this, but this book and this book, together, would cost about the same as an hour on the phone with RS staff. They would give you much more information than any conversation could. They would help you figure out what questions you might want to ask the RS people, or those on this forum. You could bring along the portions of the books related to the places you'll visit -- "a guide in your pocket." There's also a lot of good information through the "Explore Europe" and "Travel Tips" links above on this page.
When you look for flights, consider using the "multi-city" option on Kayak or another search engine, flying into London and home from Ireland. That will cost little or no more than a round-trip ticket, and save you the time and cost of backtracking to your landing city. When you've decided what flights you want, book them through the airline's own website, so you're doing business directly with the airline instead of with a third party. That can be helpful in case of any problem later.
Trains vs. cars depends on whether you want to spend time exploring countryside or smaller towns between the cities. For that a car would be best, but keep in mind that they drive on the left, which can be a challenge for some of us (like me). Otherwise, you'll do better between larger cities by train. I haven't been to Ireland, but my guess is that the best way to get between Britain and Ireland in your time frame is to fly. The alternative, a ferry, might be fun but would take much longer.