Ireland by car !

OK, let's break this down. You plan two days in Dublin - would that be your arrival day and the next day (nights 1 and 2)? Then two days in Belfast (nights 3 and 4). Then two days before the wedding, the wedding day itself, then "some time" in Galway. If "some time" is also two days, you have now used up nine of your 13 days. Is day 13 the day you fly out from Dublin? If so, it is not usable for anything other than getting to the airport. You could hit Donegal on the way from Belfast to Clifden, and you could see the Cliffs of Moher while you are in and around Galway. If you go to Dingle, getting back to Dublin will be a whole day, which would have to be on day 12. Now you are down to about two days to see Dingle, and no time for anything else, including fishing (where would you get gear?). Rather than drive all the way down there, I would suggest that you add time to Galway, Belfast, or Dublin and call it good. Driving can be incredibly slow (use www.viamichelin.com and add 25% to their time estimates to get a more realistic idea of just how slow it can be), and you are going to have to spend a lot of time in the car. You really need to look at the travel times between places to see what usable sightseeing time you have vs what you want to see.

Thank you for the info.
BTW ,we will be flying back from Shannon.

Well, that helps, but doesn't solve the time crunch very much. Day 13 (if it's your departure day) is still unusable for anything. Without the need to drive back to Dublin, you could do either Dingle or the Killarney area, but not both. Do look at the travel times, and remember that you need time to actually see what you want to see. The little details of moving around can throw off your plan if you don't allow for them.

For example, on your arrival day, it will likely be mid-morning or later by the time you get out of the airport, get your car, etc. If you don't plan to get your car until you leave Dublin (preferred), the same amount of time will be spent on day 2 getting to the rental office, doing paperwork, etc. Checking into your hotel, meal times, checking out, driving to Belfast (about two hours) and checking in there will take up roughly another half day of your two day Dublin window (or your Belfast one, if you make the move on day 3 instead). You will need to prioritize the things you want to do and see to fit the remaining time. Every time you change locations you lose time on details. If you are aware that it will happen, it will be a lot less frustrating.