1 hr layover between domestic and international segments in Madrid

It is not a connection I would want but IF they stand behind it. They may hold the international flight if they know you are coming. With a short connection don't be afraid to jump any line.

The airline is on the hook to make sure you make your
Flight connection. The EU Aviation rules are quite punishing for the airline if they don’t—so they will be sure you make your connection. If you’re really concerned tell Iberia someone in your group will need assistance getting through the terminal. Then they will send an electric cart to pick you up and transfer you.
And you can be sure the plane will be waiting for you at the gate.
Have a great Trip!

Kenko, that is a great idea! We’ll have just finished walking part of the Camino, so I’m sure we would appreciate any assistance. ;)

I'm curious/highly doubt that you'd arrive from SCQ into terminal 1. They are practically separate airports. All Iberia's flights and most (pretty sure all) of its partners operate out of T4/T4S. (We'd call T4S more of a satellite concourse rather than a full terminal of its own. All non-Schengen flights operate from there.)

If it's all T4, an hour is tight, but not impossible. You'd arrive at the main concourse, walk/travelator to the center of the concourse, and elevator/escalator down to the train. Train to T4S, up a level to passport control, and up another level to the concourse proper. Passport control is the sticking point, as many of the flights to the Americas leave in the mid/late AM and the lines can be long. Then on to the gate—AA always departs from the far end f the concourse. Also tricky: the elevators/escalators to the train aren't hidden, but they aren't well signed—I've seen couples fight in frustration trying to find them.

If you do miss the flight there will be loads of options to reroute via OneWorld partners.

If you do arrive at T1 it's almost impossible. Add a bus and security on top of the above terminal navigation.

Consolation for a delayed arrival at the final destination would be 600 euro each. But don't count on them holding the plane for just a few people— delaying the originally booked flight to ORD would cost them much more than that.

I would not want a one hour layover as these two terminals are not close together and this airport is not easy to negotiate. (See above about the signage in these terminals). Have you put your flight numbers for the next day into the "arrival/departure" option on your airlines web site. That is how I try to determine where I will probably come in and where I need to be. If you really do have to go between these terminals, get on the airport web site and research how do navigate the bus between them. Also, If you do find yourself delayed by passport control, try to find an "official" person who can help you get to the front of the line. (I had to do that in the Munich airport in 2018). If you are able to get help from someone who meets your plane, that would be the best.

There does appear to be several other options for getting to ORD should you not make the one hr. connection. The downside is they entail an additional connection.

As you would be getting to ORD more than 3 hrs later than scheduled you should be entitled to 600 euro compensation ( EU 261 rule)

I would hope for the best and be a bit flexible

Ok, I’ve done some research and it looks like the SCQ flight lands at Terminal 4. The ORD leg leaves out of 4S. It sounds like we’ll need to find our way to and clear passport control. For peace of mind, it might be worth arriving in MAD early and giving ourselves a couple of hours at the airport.

Thanks everyone!

It takes forever to get around MAD, even if you only have carry on, I would want 3 hours between flights at least. J