Welcome to FT.

Most everyone here will say AA miles, but you will likely redeem them for flights on Cathay Pacific (CX). AA does not fly to Bali (they actually fly to only a few Asian cities).

The BA "travel together" ticket only works on BA metal, so you cannot use it for AA/CX. Also, BA flights come with hefty fuel surcharges, so even if they did, you would pay >$1000 out of pocket for each person with BA Avios. Lastly, Avios prices PER SEGMENT and they are high prices for long-hauls, meaning that USA to Asia isn't a good deal with Avios.

Why not have both you and your wife apply for 2 AA Citi cards and get 100K miles EACH? With the spending, you could get 110K miles each, which is enough for a roundtrip business class ticket.