It will be a fab family trip, they'll never forget it! I have 3 kids too between age 8 and 3 so a little younger than yours but here are our favourite spots :
Slieve Gullion Forest Park in County Armagh - there is a fabulous fairy walk through the woods and it's truely magical. Also, there is a delicious coffee shop on site.
Narnia Trail at the Kilbroney Forest Park in County Down - you can walk in the footsteps of CS Lewis, this area is where he spent his childhood vacations and is said to have inspired the images of Narnia. The trail through Kilbroney takes you through the wardrobe door, by the lampost and past the tree people, carved wolves, the ice palace and of course the thrones.
I would recommend the Wee Tram Tour of the Titanic Quarter in Belfast, it will take you round the whole area and you'll stand where Titanic once stood while being built. The Titanic Belfast exhibition is great too and your family would be at a good age for it. You can walk across to the Titanic Hotel and have a coffee in the Drawing Rooms where the plans for the Titanic were drawn up.
Further on up the Causeway Coast, you have Carrickfergus Castle and on up to the Giants Causeway and Carrick a Rede Rope Bridge are all worth a stop.
Londonderry/Derry is steeped in history and you can walk along the top of the walls of the city. The Walled City Brewery has the most amazing food so I absolutely recommend you stop for a meal there.
From Derry, you could head towards Omagh and do the Ulster American Folk Park, this attraction has two parts, the first, shows life in 19th Century Ireland, you walk through the countryside to the town where you 'board' a ship to cross the Atlantic, seeing conditions for those making the voyage. When you 'arrive' on the other side, you are in 19th Century America and life is depicted with living history actors, you can go in and meet them in the log cabins.
You could try accommodation at Lusty Beg Island - there are log cabins on their own private island.
After that, you could head West towards Mayo, you could try a night or two in a Bell Tent at Westport House - it's so much fun. All you need is provided (just bring a sheet, a blanket and pillow), there is a lovely pizza restaurant on site so no need for camping equipment. The Adventure Park at Westport House is great too, you can get a day pass and do the ZipWire and Zorbing.
Depending on how much time you want to spend in the car each day ( I would definitely drive if I was you), that will dictate your itinerary. Remember, average speed is around 60 miles an hour and only a few roads are highways so you won't be going too fast. Driving on the opposite side of the road is fine, you get used to it pretty quickly. Just book a car with automatic transmission instead of a stick shift.
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