Thank you all for your kind responses!
@spidergirlBoston: As mentioned by other people in this thread, Cheapoair's price is actually higher than the Chilean version of LAN.. I did successfully booked my flight to Punta Arenas and Easter Island on Chilean LAN website, but I had trouble with Sky Airlines (now it is solved by the way).
@Toid: I successfully booked Sky Airlines from trying on a daily basis, for some reasons, yesterday's bookings worked like a charm, but like many others I didn't get any confirmation at all, so I will use your provided number to call Sky Tomorrow to confirm.
@eeuunikkeiexpat: Thank you for your info, I did know about Chilean LAN, but I wanted some flights on Sky to save money :p
@jjjason1: I successfully booked flights on sky airlines after a few more days of trying, but same as you, I didn't get any confirmation. So I will give them a call Tomorrow. Thanks!