Chicago to Ecuador help
a stopover simply doesnt exist on an AA award. it would price as two separate tickets. so add together the cost of Chicago to Colombia, then Colombia to Ecuador. you're free to stay as long as you want as long as the tickets are available.
For UA, I believe your only limit is your entire trip has to be bookable. (i.e., you can't have a 14 month stopover)
for future questions, you should search the United and AA forums on here. there is tons of information to answer most of your questions about booking award travel already on this site.