First thanks for everyone on this forum -- i have only been reading for 2 months and am astonished at the amazing deals/free flights.

I want to go from Houston -- Rio de Janeiro -- Santiago,Chile -- back to Houston -- or switch the 2 cities

1. Should I redeem my AA miles or my BA miles? I read that BA miles you can use for layovers.

2. If I use BA miles -- do i do the research first and then call BA -- do i use each stop as one way segments?

I guess Im really confused how to call BA and try to get the trip done for 40k miles. How does the award calaculate? LAN is a partner but flies out of miami so I would have to get from houston to miami or can the trip originate from houston with a layover in miami. I then read that i can add a city to the front and back of the trip as extra.

I can use my AA miles as one way trips from houston to rio and then santiago to houston but i would have to pay from the plane ticket from rio to santiago.

If someone could explain this to me I would appreciate it. My brain cant wrap around this.

I know that everyone here is experienced and i am completely knew to this. I am the person who booked on expedia and never cared about frequent flyer programs and never knew this was possible.

Im trying to book this as a suprise for my wife.

Thanks For everything

IAH-GIG; GIG-SCL; SCL-IAHBA awards are based on the award chart if all flights are on the same partner or one partner + BA. If you have more than one partner (AA+LA) then you have a mileage base award that is typically more expensive.
If you want to use BA miles for LAN & LAN-only flights you'd have to get to a LAN departure airport (MIA, JFK, LAX, SFO, CUN, MEX) & using BA miles should allow you to layover in GIG or SCL. If you chose to use AA miles you can depart from IAH with a MIA layover but can't layover without it counting as another one-way. Here's the LAN route map

First off you only have two destinations in mind, so in an ideal world you need one one-way with a stopover and one one-way without a stopover.

If you have CO or UA miles that could be helpful. I'm not sure if they allow stopovers on your way to/from a destination, but if they do that seems to be the easiest option.

If you don't have enough CO/UA miles for a round trip, but enough for a one-way that could also be helpful.

A few BA & AA mile option examples:

(a) IAH-MIA (paid or one-way AA miles redemption); BA miles on LAN for MIA-SCL; SCL-GIG -one-way ticket with stopover in SCL; For GIG-IAH you can use AA/CO/UA miles, or use BA miles, but all GIG-IAH flights would have to be on AA metal (so only one partner is used).

(b) Use BA miles on AA metal for IAH-SCL & GIG-IAH and use either BA or AA miles for a one-way between SCL & GIG or buy SCL-GIG.

(c) Use AA miles on AA and/or LA metal for IAH-SCL & GIG-IAH and use either BA or AA miles for a one-way between SCL & GIG or buy SCL-GIG.