Ireland, Scotland, Northern England

If you want to do Ireland and somewhere else - may I suggest you check out Wales? (You probably won’t be allowed to ship the car across the Irish Sea - so, go on the ferry as foot passengers and hire car at Holyhead). Stena Line & Irish Ferries operate between Holyhead & Ireland. http://www.visitwales.com

It's hard to say how much time in Ireland is enough. Personally, I can spend most of a day just doing one museum or castle, or walking a single trail. I also enjoy 'down time' when on holiday, at least when I've rented a house or apartment that I can call 'home', not so much if I'm staying in a hotel.

If you decide to head elsewhere, Wales has already been mentioned but there is also the Isle of Man, the English Lakes District and/or the ancient cities of Chester and York - all of this is in the North and worthy of a visit, though not necessarily within your 17 days!

Scotland is easily reached by ferry from Belfast, and you disembark in Galloway, which is lovely.

Which airport will you depart from? If in Ireland, that limits the time you have to spend in England.

To avoid backtracking, I'd recommend you fly open jaw: arrive either Dublin or Shannon, depart either Edinburgh or Glasgow. A flight from Ireland to Scotland would save time as opposed to the ferry.

But personally I'd want to focus on just one of the two countries with only 17 days to work with.

Depends on the people involved but you wouldn't exhaust just the southwest of Ireland in 17 days let alone all of Ireland. Would strongly advise picking just one and doing that country unless you know this is your only trip and its a lifelong dream to do both. Regardless of one or both....Just don't rat race around trying to see everything or even a lot every day. Avoid one night stays....explore an area, linger a bit and allow time for interaction with the great Irish people. Also to allow for time for you to discover things great and small on your own.

Taking the time to discover a little cafe for breakfast, with time to talk and laugh with the owner or stopping on a road to calmly look at horses grazing in insanely beautiful scenery and to end up talking with a farmer and being invited to his home for tea after helping to feed the horses is SO much better than frantically racing from one tourist spot to the next.
We usually pick one thing to do a day with some other ideas in case we have time, but absolutely never pressure ourselves to see the next thing.......because if you're really looking the magic is right next to you, not down the road.
That being said in order to give a recommendation on where to go and what to do.....need to know what you enjoy ? Cities/villages, scenery/shopping, urban nighttlife/trad music, ancient historical spots/modern attractions, fancy dining/rustic pub food etc.
We had an acquaintance who really could care less seeing dark age ring forts/castle ruins or ancient burial mounds. For her it was old stuff....who cares. An attitude totally beyond me...incomprehensible. She wanted fancy shopping outlets and trendy clubs......something my wife and I would loathe. But to each their own. Let us know what are your areas of interest and this forum is excellent with good advice and ideas.
Hope you have a great time. It really doesn't get better than Ireland !

Ewewoolknit-you give excellent advice! I concur!

17 days is NOT too much in Ireland. I did three weeks and probably could have spent at least a couple more. I would not try to see Ireland along with parts of England or Scotland as that wouldn't give you time to really see anything. With 17 days you will be able to spend a few days in each place and take your time. For flights consider three places: Shannon, Dublin, and Belfast. Fly into one and out of the other. I flew into Dublin and out of Belfast, but I didn't rent a car so was relying on the train and bus to get around. If you start in Dublin you could do a loop by heading south, then across to Dingle, up to Galway then north and eventually end in Belfast. There is a woman who specializes in Ireland travel and will do a driving route for you for a fee, the web site is irelandyes.com.

17 days is absolutely not too long for Ireland. I've gone twice, once for 10 days and once for 11 and I haven't begun to see everything I want to see there.