Welcome to FT, mitpianoman!
Unfortunately, skipping any leg of an itinerary will cancel all remaining segments if they are on the same record locator (even if they are on separate airlines). I would not take any risks with this by skipping GPS-GYE on your reservation.
As for the "country connection," I'm not quite sure, but it may have to do with the fact that you'll be flying LAN Ecuador, which is still LAN, but operates under a different name.
Was this booked as an award ticket?