I am planning a family trip (2 adults, 3 kids) to Brazil for the summer of 2015. I know award availability is pretty terrible for Delta, but I also know I have a few other options on their travel partners. I am fairly new to award travel so I'm wondering what some of the more seasoned Delta award travelers think about the possibility of doing the following:

Travel DTW to LAX on Delta. Stopover in Los Angeles for about a week to visit family. Travel LAX to GRU (Sao Paulo) on Korean Air direct flight. Then travel GRU to BSB (Brasilia) on Gol to our final destination. The return flight home (DTW) could either be through Korean Air, AeroMexico, Delta, or some combination.

Is there any chance on piecing together 5 low-level economy award tickets for this? I think I could get the DTW-LAX segment on Delta, but I'm not sure how many economy award seats are available on either AeroMexico, Korean Air, or Gol.

If doing this seems implausible, I'm thinking I may want to think about earning award travel through a different airline (United or AA perhaps). Any advice/ideas would be much appreciated.