Why in the world you want to use Avios?! It is a whole lot more expensive than using AA miles both in terms of miles and in terms of cash.

Using AA miles for a sample itinerary SFO-HKG-SFO, it is 55K one way in J and 67.5K one way in F. The cash portion is either $2.50 or $5.00 outbound (I dont remember which one) and about $38 inbound.

The 3 years old would have the same cost as the adult. The infant would pay a % of a published fare of the cabin s/he travels in - so whatever the adult redeems, it would be X% of the fare for the infant - though it has not bee a clear cut matter whether it is the non-restricted fare or the discounted fare. You would need to call AA to find out. Or search the AA forum on the topic. It has been discussed many times in the past so you should be able to find multiple threads on it.

As several posts pointed out, SPG pts to AA miles would be the no brainer option.