I've flown my family with 2 young kids, AA FC from NYC to Maui, 4 times and to NY to San Diego once AA FC. The first to Maui, not knowing what we were doing, flew Ny-LA-Maui, in 757s, which in FC is nothing to write home about. Then the next time through Chicago, we got in a 763, which had the better FC seating(leg supports) and now the super nice flat sleeper compartments with the music and TV as mentioned. It is my understanding the AA uses the 763 and 777 for most Int'l, so you will have the better planes.
With our first FC experience, it was much nicer than coach, but nothing special. Then when we found the better planes, it made a huge difference in our vacation experience. Make sure to take plenty of pictures or video as we did, because you and your daughter are in for quite an experience. Your daughter will especially love the special environment and attention.
The best way I can describe the difference is that in FC, your vacation starts, as soon as you get to the airport, whereas in coach, at least to me, your vacation doesn't start until you get off the palne at your destination. FC just allows you to start destressing immediately, and your mindset starts changing right there.
With the said, I also think you used it for the right kind of trip. In hindsight I wish we flew coach to San Diego, because domestic FC isn't worth the miles in my opinion. I'm even questionng flying FC NYC to Aruba next Feb. I don't think for NY to Aruba AA flys 763, so in a 757 FC isn't worth it, as the miles will be better spent on our next Maui trip.
Anyway in my opinion, miles well spent.
Regards.