Trains in the North West and Wales have been susceptible to more than average planned strikes/stoppages over the last year, I have been to check with the information point at the main station here, and none are planned for the period in question. Here is the railway timetable site, which you may find useful: www.rail.co.uk/ukrail/planner/planner.htm.

I've just been in mid-Wales for the week, it's gorgeous, I would love to have shown you round, but you do need a car.

Given your time span, I would split your time between London and Dublin - for me, the bias would be to the latter. Ferry crossing would not be a problem, but neither would flying, and that would give you more time in both.