I am more familiar with BA award chart however just flew their OneWorld partner LAN from JFK to Easter Island w/stopover in Santiago one way and the return ticket (separate one way) from Easter Island w/stopover in Lima back to JFK. Easter island not good for toddler IMO but trick is to avoid Chile $140 visa fee if you can, I paid it as Santiago was entry into Chile. AA is OneWorld look at LAN options w/stopovers in South America. one way tickets may be good - you can split reward tix. Since distance based look at LAN out of Miami to save some miles. i wasn't able to do AA to MIA and switch to LAN hence direct from JFK. Their J product was quite nice, I actually slept w/lovely duvets and had good meals surprisingly.
I'm in Philly do I'd look at United partner USAirways to Italy, they do seasonal to some cities but direct from MCO. Lots of Philly options many are not aware of-
Not sure of your location or timing but hope this helps a bit