Travelling to Spain for 6months - EU passport and American passport

Your question(s) are best directed to the Spanish Embassy/Consulate.

Just my guess but I suspect 90%+ of what you will get here will be primarily speculative and most of the rest 3rd hand hearsay.

Ditto, contact the nearest consulate:

http://www.exteriores.gob.es/Embajadas/WASHINGTON/en/Pages/inicio2.aspx

I’m American, and have recently discovered that I don’t need a visa since I’m travelling with EU passport holders...

I'm highly skeptical that this is a Thing. Or, at best, there's gotta be more to it. Just imagine the opportunities for abuse.

But as others have suggested, you really need to get real information from a real source. Contact the embassy or consulate of Spain.

Is your husband working In Valencia?

The legal position is set out here: https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=LEGISSUM:l33152

Kristin, An EU citizen (your husband) has the right to live and work in any EU country, and bring his non-EU dependents with him (not "travelling with", "living with"). Exactly how this works is different in each country. It probably involves him registering as a resident in Valencia, and declaring you as a dependent. Ergo a lot of paperwork (including Marriage certificate), probably similar to that needed for a visa, and only the Spanish consulate can give you a definitive answer.
If your girls have EU passports, they can stay as of right.

This will mean you become Spanish residents, pay Spanish tax, Spanish health system etc. As you are legally moving there, no problem of return flights.

Problem 2: The UK leaves the EU in March 2109. That implies no more EU citizens rights in other EU countries for UK citizens. Exactly what the system will be and how UK citizen visitors will be handled is one of the thousand-and-one open points. Will UK citizens have their passports stamped and be subject to the 90-days-in-180 limit? Nobody knows, and plenty of people want to know, including me.
But you say your husband is also Irish. Make sure he (and your daughters) have Irish passports and do this all as Irish citizens, not UK.

Just to avoid confusion, even though it's probably obvious, Chris meant March 2019 - in other words while you are planning to be in Spain.

Be sure your girls have US passports, too, if you are planning to return to the US afterwards. We once forgot one of our kid’s US passports, only had his other passport, and he was almost denied boarding—long boring story involving a seven -yearold.
As for you, I’d think that whoever is sponsoring your husband would know, but I’d still contact the Spanish Consulte office for your area for accurate information. Consulates handle this rather than embassies.