I make sure the boxes are both clean and unobstructed. *When I catch
Aster in the act I scold her and pick her up and put her in her own
box. *I think she partially doesn't "get it" and partially it's a game
to her. *And who knows what goes on when we're at work all day.

Any advice besides correcting her 'in the act' and making sure the
boxes are clean to STOP one cat (Aster) from using the other's box?
Ezzie had been alone for the first 6 years of her life so we don't
want to make them share a box even though many cats do. *Plus, Aster
has a sensitive stomach. *We've had her tested for everything and they
say she's healthy, but knock on wood, if something does ever happen we
don't want any diseases passed back and forth, or just germs in
general.

Basically, you can't stop her from using another litter box. (It's
better she uses another box than the floor or another undesirable
place, like your bed.) Please don't scold her when she uses the
"wrong" box. She might start being more secretive about going in other
locations. You can add a third box near the "wrong" box to see if
she'll use that. Some cats like to urinate in one box and defecate in
another box anyway, so you should ideally have three boxes for two
cats.

I am unsure why you don't want them sharing a litter box. If you scoop
twice per day and regularly scrub the boxes, there is little chance of
disease transmission.