OP, if I were you, I would explore the possibility of just redeeming two awards for each one-way on AA. It's 70k AA miles to get to SE Asia in business and another 40k to get from SE Asia to Australia in business. That's 110k miles each way, per person, in business class. Use British Airways' website (you'll need to register a new account) to search for oneworld partner availability. Make sure you search segment-by-segment, otherwise you may get incorrect results.

You can also think about transferring your SPG and MR points to Singapore Airlines. There you can redeem one award to get your family one way in business class from the US to Singapore to Australia. You'll have to pay fuel surcharges, but they're not too steep and the number of miles required is low compared to American carriers (plus the 15% web redemption discount).
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