I'm an Englishwoman who's married to an Irishman and has lived in Ireland for nine years so I hope I can help a bit.
Ireland is a great place to visit, as long as you accept that it can rain at any time of year! But it is beautiful, friendly, has amazing history and is like no other place in Europe. I love it here and wouldn't want to live anywhere else now.
Southampton is not a major airport, but you can fly from there to Dublin with Flybe (www.flybe.com
). Otherwise, from London Stansted you can fly to Shannon or Dublin or even Cork with Ryanair or Aer Lingus. I am sure there are other options too. You can fly home easily from Shannon.
I wouldn't recommend train and ferry to Ireland - British trains are extremely expensive and I don't think there is an uncomplicated route. Ferry travel can be grim -I absolutely hate it and avoid it at all costs unless we really must take the car on visits to England. We will have to do so this June on our way to Southampton for our first ever cruise on the Med - we can't wait for the cruise, but I'm not looking forward to the ferry!!
Once in Ireland, hiring a car is a great option and gives you lots of freedom. The roads are fairly quiet outside the cities, but the surfaces may not be what you are used to! You also need to remember that it takes longer to get everywhere than you might expect from looking at the map as the roads are usually single lane and can be winding, and you can often spend time stuck behind a slow vehicle that your can't overtake. That said, driving here is generally fine.
I know of one tour company you could try, run by a guy I know called Dermot Buckley. His website is www.dbcsireland.com
and he operates out of Shannon and Dublin. I've no personal experience of his tours, but I know Dermot and his family because they live near me and our kids go to the same schools. He's a really nice guy, a qualified tour guide with a great knowledge of Ireland. At least his website will give you some idea of the type of tours that are available.
There is so much to see in Ireland it's difficult to know where to start. Dublin is great - you'd need at least a couple of days to get a taste. The prehistoric site of Newgrange is reasonably close and is fascinating. In the South the must sees for most tourists are those in Cruise Fanatic's reply, and I agree about Dromoland Castle - I haven't stayed there but I have eaten there a few times & it is amazing. It has a website - worth a look.
I hope you manage to arrange your trip and I hope you all have a wonderful time!