Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
How many is "we"? What class of service?
If you use BA Avios on either AA or IB, you will be charged hefty surcharges. But if you open an Iberia Plus account now and fund it (by earning miles on it or converting some MR points to it), you will be able to transfer your BA Avios to Iberia Plus after a 90-day waiting period. If you find award seats on IB's season LAX-MAD nonstop, you will then pay only modest surcharges.
Another possibility is to use BA Avios to fly LAX-DUS-MAD on AB; there are no surcharges when redeeming Avios on AB.
Whatever you do, don't transfer anything any where until you are sure that the award seats you want are available.