The bilateral treaty between Spain and Venezuela allows for up to 3 airlines from each country, not two. It was signed in 2000 and came into being in 2001. That enabled operations from Air Europa. The third designated Spanish carrier was Spanair but never ever took up the rights. I have not seen any official statement from the Spanish Foreign Ministry requesting authority for Air Madrid to start services to Venezuela and fill in the gap left by Spanair.
On Venezuela's side, designated carriers were Avensa (now defunct), Santa Barbara airlines and Aeropostal. This last airline, despite having traffic rights to the UK, France, Germany, Netherlands and Switzerland, never ever bothered to fly with its own planes and just opted for a code share agreement with Air Europa on the Caracas-Madrid leg. This was abrogated, on the Spanish side, as far back as November 2004 after a very difficult personal relationship between the owners of both airlines.
For your information, Los Rodeos (TFN
) is not usually regarded as the international airport for Tenerife. That is the role assigned to Reina Sofia (TFS
) and Avensa services used to be handled from there.
Now, S3 has an exclusive right to use it as its owners are from the Canary Islands, are influential in local government through Coalición Canaria and own the only real competitor to Binter Canarias (Islas Airways). Remember Venezuela is very much regarded by the people of the Canary Islands as the "8th Island" (no secret that at one point in the 50s and 60s there were more inhabitants living in Venezuela from the Canary islands than in the islands themselves !) and the González family gets preferential treatment in very many ways.
Hope this clears some of the points you raise and I repeat what I said in another thread: Aeropostal's problems begin and end with Mr. Ramiz.
Greetings from Cancún !