understand your point but a Nationalist regime in Spain might desire to unite Iberia and think themselves more deserving of colonial empire than Portugal? Germany did not try to establish a "common market" with Austria after all. the main tungsten mine is also near the border which makes it even more appetizing target. (and OTL they actually had to pay in gold for it, IIRC something approx. 200m US)
(btw read War for Oil, Nazi quest for an Oil Empire and oilfields of Romania were considered almost a German resource, not just by Nazis, they DID plan on seizing them if necessary)
The Austrians by and large wanted to join Germany and considered themselves German. It was the Austro Fascists who were fighting AGAINST this Pan-German sentiment and convince the population to be Austrian Nationalists, and even that had to be spun as them being "Better Germans". And yes, the Germans were prepared to seize the mines IF NECESSARY; they were a vital strategic resource, after all, but they diden't have to because they finagled the supply peacefully. And it resulted in getting the output undamaged, Romanian military support during the war, ect.
For the invasion of Portugal... do you honestly think the military action required to take and hold the mine (Which would ultimately require a conquest of Portugal) plus the cost to operate it isen't going to cost more than 200 million USD? To say nothing of the diplomatic bad-boy points you'll be getting for such an action: in the event of a successful qucik coup back by the legitiment government, the Spainards are probably still going to have access to the international market where they can actually make use of their gold/treasury (Fat lot of good saving it does you if you can't exchange your commercial paper for something actually useful in war), especially from raw-resource glutted and market-starved South America. Invade Portugal and US influence is going to be slamming that door shut.
And before you say "They can just conduct a quick, splended campaign to seize the mine"... no, Portugal would seek international assistance, particularly from GB, and fight back. This would cost more Spainish lives and money directly to defend and police the areas, to say nothing of the rise in cost of production of sabotage/infastructure damage/collaterial damage from battles in the area as the Portugese struggle to regain their country (At minimum, they'll be bombing you with whatever they can muster).
As for uniting Iberia and wanting a larger colonial Empire... sure some elements of the country might. But the classical conservative elements and corperatists in the Right-Wing coahalition that was the Fascist regime? Not against their ideological mirror in the former case or at that cost for the later. The Carlists don't care, the Liberals-Old Government Centerists who're going to be sticking around if you want to pull off the quick coup and subsequent quick reassertion of control over the state and crackdown on the Communists to prevent a civil war/police action of a fair scale don't want to. Not all Right-Wing elements of the era were Imperialists/Autarkey focused; in Spain the legitimate "Nazis" (or as close as you're getting) are the Falangists, who are more anti-Communists and domestic-focused than expansionist like the Italians and Germans were, and are vastly out-numbered and out-organized by the more numerous/better armed/better respected military establishment who were the glue that held everything together. Good luck having that minority manage to get their way.