Layover and Immigration/Customs

Immigration/customs will take 30 minutes to 2 two hours depending on how many flights arrive at the same time as yours.

You will have not have to collect your bags. To make sure the bag tag and claim check will have the three letter airport in Spain listed on it (e.g. BCN for Barcelona). It looks like there is a Left Luggage service at Dublin https://www.leftluggage.ie/

On the way back you will go through both the Irish and USA immigration/customs before your trip to Chicago.
Dublin is one of several overseas stations where the USA Customs Border Protection has an office
3 hour is enough as long as the flight from BCN is not severely delayed.

On the way to Spain, I have been told that our checked luggage will not be unloaded and then reloaded when we arrive in Dublin because we are traveling on a single ticket though a single airline (Aer Lingus). I assume we will need to go through both immigration and customs.

Customs is the check on the contents of your luggage, whether it contains anything liable to customs duty (taxes) or banned. As you will not have your luggage with you in Dublin it cannot go through customs there.
You will go through immigration (passport checks) when you enter Spain, and your passport will be stamped (if necessary) for entering the Schengen Area. You then pick up your luggage and carry it through customs (random checks only).

What happens at Dublin depends on whether you decide to go into the city. If you stay "airside" inside the airport, you will not officially enter Ireland, and you will not go through any passport checks.
If you want to visit Dublin, you need to exit via immigration, and have your passport checked and if necessary stamped for entering Ireland. When you return to the airport, you will have to go through security, and passport checks for exiting Ireland (possibly another stamp) in order to get "airside". Be sure to allow enough time for this (at least 1 hour).

And can anyone confirm that we don't need to get our luggage and recheck it the way we have to in the US?

That is normal. It is only the case in the US because you are changing from an international to a domestic flight. In Europe, intra EU bags have a different luggage label so those transferred from outside can be recognised at the final destination (Spain), and your luggage goes through customs there.

On the return trip, we have a 3 hour layover in Dublin. Do we go through immigration/customs before our trip to Chicago? Is a 3 hour layover okay?

As above, not if you are staying "airside". 3 hours should be enough.

Thanks for the quick responses!