In this case, EF was correct. However, I was mistaken: the original airpoints customer service rep did not lie to me. She told me that there was no availability in PE seats. When I called today, they told me the same thing. The woman said, "I can only see what is available to you. Everything else is blocked out."

So I explained that I knew there were open seats, I was travelling with a 3 year old, who did not need luggage and who did not need food on the plane. I couldn't see having to spend an extra $100 just so that we could both sit in the PE area. I explained that I either wanted a refund so that I would be seat + bag, as I wasn't going to pay $50 for just a meal, or they could move me up to PE with my daughter.

The rep said she would have someone look into. Sure enough, later in the day, I checked and on the return flight, I have been moved into PE.

Lesson learned: they are really strict about this. If it hadn't been the fact that I was GE and the other passenger was just a 3 year old (who clearly didn't need the trappings of works), I don't think they would have done it.