crossing Argentina and Chile borders

That's a bit of a zig zag. If you are starting in Santiago and want to see Pucón and Puerto Montt, it is much quicker to go down Chile and cross into Bariloche at Osorno. Plenty of bus companies do the route. Then you could bus from Bariloche to Mendoza. If, however, you want to do the over the Andes trip to Mendoza from Santiago, I see your problem. One way would be cross from Chile to Mendoza, bus to Bariloche and then cross to Pucón from San Martin de los Andes (one bus a day except Sunday at this time of year), bus to Puerto Montt from there, then cross back at Osorno to Bariloche (more frequent service on this route). This leaves you in Bariloche however. You'd have to backtrack to Puerto Montt if that's where you want to end up.

From Mendoza to Pucon, by far the fastest and cheapest way is through Santiago.

To get from Mendoza to Pucon, you could also catch a bus to Neuquen, catch another bus to San Martin de los Andes, and another to Pucon. You may be able to go from Neuquen to Pucon direct, as I'm pretty sure the bus we took from Pucon to San Martin continued to Neuquen.

Hi I would say the best way to do this would be to head from Santiago down to Pucon about 12hrs bus ride if I remember. The from Pucon we got a bus from there to San Martin de Los Andes. We stayed overnight but you can get a bus straight to Bariloche if you want another 4hrs bus ride. I cant remeber how long it took to get from Pucon to San martin but I can remeber it took ages to go through customs at some remote border crossing!!!. It was a really scenic bus ride though. When in Pucon you can get buses down to Puerto Montt. There are lots of border crossing points between the two countries but I would recommend going down Chile and up through Argentina. Enjoy its a fantastic part of the world.