Customs & Immigration Traveling ORD to DUB to LIS - Non-Schengen/EU vs. Schengen/EU

H all! I have been following this sub for a while, but just haven't posted anything. I did do searches and reviewed the sidebar/FAQ but couldn't find anything specific to this situation. (Apologies if I missed something.)

I'm sure this happens all the time since it's an itinerary that can be booked on one ticket, but couldn't find anything on it here or elsewhere. (Government and airport sites seem to be equally unhelpful or confusing.)

To get this out of the way - we've traveled internationally many times before, so tend to do a lot of research to alleviate anxiety, and just be well informed. We have our itinerary booked and all, so don't need help with that.

I just have questions about this itinerary since we are flying from the U.S. to a non-Schengen but EU member country (Ireland) with a layover. Then, continuing on to a Schengen and EU member country (Portugal).

Some info:

• We're flying Aer Lingus (ORD > DUB 11/8-11/9, then DUB > LIS in the afternoon of 11/9). (Do you want the flight numbers? That shouldn't matter for my questions below, but happy to provide if necessary.)
• We have flown through Dublin before, but only on the way back, so we're familiar with U.S. Pre-clearance coming back. That's on the way back, anyway, my questions are about flying to these countries.
• My wife and I are both checking a back and we'll have small-ish carry-ons, including a piece of medical equipment I've never had an issue with before, it's just annoying to lug around and I like complaining about it.

As scheduled, our flight lands at 0900 in Dublin, and our next flight doesn't leave until 1515 - a little over 6 hour layover.

So, primarily two situations could happen, especially now with the air travel issues in the U.S. because of the government shutdown.

First Situation - The Preferred Eventuality Our plan is to be able to leave the airport for a bit. Likely we won't risk going into Dublin itself, but may hangout in Swords or somewhere else nearby for breakfast/lunch. In this situation, I assume that we will go through passport control, customs (with only our carry-ons, since the checked bags should be checked through to our final destination), and then exit the airport after possibly stashing some stuff in a locker, like the aforementioned annoying medical equipment.

Once we get to LIS, we would go through passport control, grab bags, go through customs, and exist, like our other trips to Shengen countries, I assume.

We shouldn't have to touch our checked bags if they are checked through to LIS, correct?

Second Situation Given the ever-increasing liklihood that our flight will be delayed out of ORD, if we stay inside the airport at DUB, what would the passport control/customs situation be, given Ireland's membership in the EU, but not being a member of the Shengen zone? I assume our checked bags would still go through to LIS. Would we have to go through passport control/customs if we don't leave the airport?

From my experience flying back through Dublin a couple times (both times were from CDG in Paris > DUB > U.S. Pre-clearance > ORD, there didn't seem to be any issues there going from a Shengen to a non-Shengen country, but I can't remember fully). But, we have never flown to Europe with this particular situation.

(Sidebar to flying back, we do have Global Entry, so hopefully coming back to the U.S. will be smooth, just got it after our last trip earlier this year but haven't gotten to use it yet.)

To help alleviate my anexiety, I'm sure someone has knowledge into this situation to help. :) It's probably not as complicated as it is in my mind, and feel free to tell me not to worry about it.

Bonus I don't think DUB is a huge airport, but if anyone has any idea how much time it generally takes to go through passport control/customs if we want to exit the airport, then again come back into the airport to hit our ongoing flight, that would be awesome.

In summary, is there anything out of the ordinary because of our layover location (Ireland) being a member of the EU, but not a Schengen member country?

Any thoughts, notes, ideas, experiences, etc. would be greatly appreciated!

(Apologies if the formatting isn't quite right, I don't often post on Reddit. I will fix it if I can after I post.)