Upvote:1
I don't foresee any problems as long as you put your actual departure date and flight from Bogota on your Colombian visa form (if applicable).
All a country generally wants to know about is how and when you arrived and how and when you're leaving.
As for the airline, again i don't foresee any problems (assuming that the NYC-santiago/bogota-NYC is a separate ticket to the santiago-bogota ticket and not just a multistop booking). As far as the airlines are concerned these are two independent bookings.