If I have understood you correctly, you were booked to fly JFK-MAD-JFK on IB (bought on BA.com), 4 pax.
Then, you got denied boarding (due to overbooking) on the return MAD-JFK leg, and finally rebooked MAD-LHR-JFK, two in PE, two in Eco.
If that is correct, your claim needs to be directed to IB (operating carrier). BA will do nothing.
You'll need to fill this complaint form:
https://www.iberia.com/us/customer-relations/
Stating the basic facts (you were booked in flight IBXXXX on XXday, were denied boarding due to overbooking etc etc etc). Don't bother writing long paragraphs, they'll ignore it anyway.
You are due to be paid EUR600 x 4 (denied boarding) plus two partial refunds for the downgrade from PE to Eco. Cite to them EU261 regulation.
The most common ocurrence is that they will ignore your claim and send you a random note. Do not get angry or reply to them, just fill a claim with the Spanish Air Aviation Authority here
https://sede.seguridadaerea.gob.es/S...aspx?idioma=en
After that, they will likely pay. If not, I am afraid you will have to hire a Spanish lawyer and claim through the courts.