You're missing a lot...but it's really not difficult at all.

You can do this without much effort and hit all three destination regions without much effort

1. Get BA Visa 50K (25k w/1st purchase) - redeem whatever miles for a one-way to somewhere exciting in SA with a direct connection to Europe on a *A carrier.

2. Get the UA Card - get the 50k bonus then figure out some way to get the extra 10k you need for a redemption to Asia, which is 60k (broken into two one-way trips). Then route the flight to somewhere enjoyable like BKK or SIN, but I wouldn't choose my summer home in TSN. You will be glad to know that *A hubs are permitted stopover points, so maybe ZRH or FRA or MUC interests you. Then you can go home

* - I don't use UA miles, I use US so please correct me if this isn't possible.....

It should look like this:
USA-SA - About 20k BA miles
GRU-FRA-(STOPOVER)-PEK (Seemingly infinite Y availability per KVS....LOL) 30K UA
PEK-USA 30k UA miles.

The UA experts can weigh in on this, but I think you can have your return leave from a different city than the one I chose for you, PEK, meaning that an example return can be SGN-NRT-LAX. I also think you might be able to get another stopover on the return too, but I'm not a UA expert. I just know that for the purpose of this itinerary, it is easier to get the required UA miles a lot faster than the US miles (well, not that much faster...).

You need to apply for the BA visa (or AA too with higher mileage required) (or be able to afford a cheap fare to a nice place in SA)

You also need to apply for the UA visa.

You then need to learn how to search *A award availability (but you need to wait until you get the miles to ask us what this means)

Links can be found here by searching.