As mentioned, you can't redeem AA miles for that.

You are going to run up against three issues.

First, finding 4 F seats will be very hard if not impossible. Suggestion, let the adults sit in F and book the kids in J/Y. After all they can't drink anyway.

Second, BA fuel surcharge. It will be very high. Avoid LHR/BA

Third, routing rules. One source says you may only stop in SIN or BKK, but another says you may stop in SIN, BKK, HKG, NRT, KIX. But it does not appear you can stop in DXB.

I'm thinking your best bet is to try and find seats on CX from somewhere in europe (other than LHR). I'm not sure which flights offer F anymore check the CX forum, but I'd guess CDG does. Anywhere that still uses a 747 will have better availability with 9 seats.