Lisa - from DFW you can take AA to LHR by connecting through ORD/JFK/MIA/LAX/BOS and then take BA6984 to AGP. Just leave enough time to connect through Heathrow as you'll need to change terminals. Another option is to fly AA or Iberia from the US to Madrid. Then take an Iberia flight to AGP.

On the return, if you connect from Europe through LHR/LGW, you can avoid the GB departure tax by having the agent mark you as a through (T) traveler in Sabre. That'll keep the NRSA system from deducting the tax out of your pay check. Just present your OA boarding cards to the AA agents. Make sure you save those for later in case they mess up and you need to claim a refund.

Matt