Sometimes there are magic bullets. May be I am looking not fly for free, however may be there are some ideas. I know my options now: just take what you get. Anyway if I would think this way, never could collect miles as an example.

To reduce fees for 3-4 flights, I would try to book for myself economy and 2 more in bus for wife and infant, here your eco ticket will save 1.5k + there is a chance that you can fly in bus with a child, if child has a seat as adult and will spend time in LAP. I think some of you saw how people sometime change their places in a plane even from economy to bus with family during "night". From crew perspective, does it matter if you sleep with a child or seat there. I don't think so.

Also if I would know that in advance, that child could bring high fees, I would try to collect miles with airline which operates this flight. I booked tickets with Etihad miles and paid 6k+20 EUR for reward ticket in LAP Online. Was easy and fast. Bad that they don't allow to buy a new ticket using miles if I got a tickets from another system. So smart move would be to book a roundtrip ticket for my wife and child first place instead buy 2 one ways for me and my wife and lap ticket for infant. I should book in AA and my wife with Etihad.

Also may be some other companies ask less fees for infant. And it is always not clear how much you should pay, you always have to call.

So noone here who did "part of around the world" with miles and with infant? What was the best option to book? Pay per segment or found out how to do it roundtrips, assign to each segment and did as roundtrip?

So I am still looking the way and still optimistic)