From Belfast to Galway area to Dublin

Many on this forum advise against driving while jetlagged (DWJ, I guess that would be). Plus, have you considered that you are intending to cross a national border with your rental car? Check the Travel Tips on this site for details about fees & regulations for taking a car across the border.

If you don't want to spend any time in Belfast, you could take train or bus to Galway, then get your rental car in Galway next day. Or, heck, if the only stops on your itinerary are major cities (Belfast, Galway, Dublin) then you don't need a car at all.

Thanks for your help. We are looking to get into Galway later in the evening but wanted to make stops between Belfast and Galway during the commute. I believe a car is best because the train goes to Dublin first. We will eventually end up there.

I don't understand your proposed itinerary. If you intend to eventually wind up in Dublin then why not just fly into Dublin (from Reykjavik, I assume, per your previous post). Flying into Belfast just adds a layer of complication to your journey, especially since it sounds like you don't plan to spend any time there. The drive from Belfast to Galway will take you nearly 5 hours, only to spend one night in the vicinity and then backtrack to Dublin if I'm reading this right.
Add to that the punishing one-way international drop charge for the rental car, and the fact that you'll be better off just dropping the vehicle at Dublin airport before venturing into the city, where you really don't need (or want the hassle of) a car, and it would seem that your better course of action is to fly into Dublin, take the train to Galway if you're adamant about going there ... even for only one night, then returning to Dublin to continue the remainder of your itinerary.
Just a thought.