Hi @841facb85ecb9fb7! I see what you are trying to do and it's a tricky thing to say the least. I don't think its feasible but lets speculate a bit.
Now the first thing to realize is that even if you get several Origin clients running only 1 client can be logged into an account at the same time (to avoid people sharing Origin accounts most likely) so as a minimum you would need the game added to both your and your wifes Origin account.
As for Aster, I don't think that will work with complex AAA games like Battlefront II. I think the 2 game instances will conflict with each other within the same operating system.
The only way I see this running is software virtualization, but not ordinary virtualization (like virtualbox.org which is free) as that would slow down the game too much.
So, the only way I can think of is using something like unRaid, you can see a video from Linux Tech Tips about it here:
This is the only way I can think of right now. It way more difficult compared to just the game having split screen I agree, but sadly we didn't get split screen this time around. Perhaps not enough people would use ☹️
