I've flown with Aer Lingus several times (Chicago-Dublin-Glasgow).
Your bags won't be a problem. They're checked through, though consider how much carry-on baggage you'll have, because there's a lot of security to go through at Dublin. You have to go through security when you get off the plane, as well as when you get on the next flight. So, if you've got a lot of stuff with you, it just makes it a bigger chore.
Also, keep an eye on the transfer times. Passport control at Dublin can get really backed up, and I've missed a flight in the past because, after a ground delay, there simply wasn't enough time to make the connecting flight. Whenever possible, I try to leave at least 3 hours' layover time.
Also, on your way home, make sure that, before you actually go through the checkpoint to enter the U.S. departures lounge, you've had a bit to eat/bought whatever you want in the main terminal, because there's only one little shop in that area, and they don't have much. And once you're down there, you're kind of stuck.
ETA: With regards to the whole immigration issue through Dublin, I think the only thing to really be aware of is that, on a subsequent visit, if you arrive directly in the U.K., and go through U.K. immigration, they'll likely ask you why you flew through Dublin the last time. It kind of threw me when they asked, but I just told them 'Because it was cheaper' and there was no problem.
The key, as when crossing any border anywhere, is to never lie, and to do what you've said you're going to do. Don't overstay.