If the Argentine government had a warranty that Chile won't invade if the Patagonian troops are sent to Malvinas.
IOTL, and I telling cause I have relatives and friends who were in both places(Patagonia and Malvinas), the troops sent to Malvinas were mainly from Northern Argentina(there we have some jungles), a place where having a day with less than 20°C is very unlikely. Besides this, the troops sent to the Islands had barely started their training, had no appropiated clothes and most important, weren't trained to stand the cold. Because of this, their morale was below 0, they were frightened, freezing, hungry and didn't now what to do. I can recommend you the film "Iluminados por el Fuego"(Blessed by fire) to understand this better.
Now, if you send the troops that were in Patagonia, and where trained to fight and stand in the cold, the British could very well got a bloody nose in the ground fight.
Going to the Vietnam like part, there's no way the British could succeed. They could take Tierra del Fuego, some coastal cities in Patagonia but nothing more. They would have easily overextended. And Argentines are very good guests with Invasion forces. The Brits learnt this a long time ago.