Only anti-realists think hidden questions lurk behind the concept of 'reality' [that's a fair definition of anti-realism]; realists take 'real' as primitive. You feel confused because you want an anti-realist account of "real," despite being a realist yourself . (Or else, you're an anti-realist smart enough to see through the extant anti-realist theories.)

Quine's is a famous example of an anti-realist account. Quine said the concepts denoting existing things (those that are real) are those variables you must quantify over in the best scientific theory of the subject. The problem with that is that "best scientific theory" isn't specifiable except with reference to what's real, although Quine made a noble effort.

When you ask whether atoms are real, the question doesn't concern the best explanatory framework; what's real determines best explanatory framework rather than the other way around—at least that's what realists think. The best theory is the one that best accounts for what's really there; the best theory doesn't doesn't determine what's real. Things may exist even though our best theory says otherwise. To parry the attack, the anti-realist can only retreat to epicycles—say, the best theory in the idealized long run—introducing concepts more problematic.