Does this mean that if I move, attack kobold 1, and divine challenge kobold 2 (who's two squares away), the divine challenge has no effect except to keep me from using DC next turn?
Yes, this first interpretation is correct.
Remember that the Divine Challenge persists until the paladin specifically challenges a different target or fails to engage the challenged target.
The phrase "you must engage the target you challenged
or challenge a different target" does not mean that challenging a different target
by itself is sufficient to meet the condition. Rather, this caveat is included to account for cases where the paladin challenged a target on the
previous turn (and did, indeed, engage it that turn), is
still challenging it at the start of his current turn (because the challenge persists until he ends it or fails to engage), but the paladin wishes to use this turn to challenge
and engage a different target on this second turn.
For example:
Turn 1: The paladin challenges Orc A and engages Orc A (by attacking this orc or ending his turn adjacent to this orc).
Turn 2: Because the paladin
did engage Orc A on Turn 1, he is
still engaging Orc A at the start of Turn 2. He now has two options for how to spend Turn 2 without losing his Divine Challenge ability on Turn 3. He can either:
(a) engage Orc A once more on Turn 2. This will meet the requirements and cause him to still be challenging Orc A at the start of Turn 3.
or
(b) use Divine Challenge on a different target, say Orc B, and
engage Orc B on this same turn. He will then still be challenging Orc B at the start of Turn 3.
He
cannot, however, do the following:
(c) use his standard and move actions for other unrelated things, and then end his turn by using his minor action to challenge Orc B.
If he could do this, it would open up the same abuse that Divine Challenge was rewritten to avoid - challenging a target and running away. Observe:
Paladin Turn 1: The paladin does something or other and then challenges Orc A (without ending Turn 1 adjacent to Orc A).
Orc A Turn 1: Orc A is challenged and cannot attack anyone but the paladin without taking damage. He is forced to either move to the paladin (possibly taking opportunity attacks in the process) or waste his turn doing virtually nothing (or suffering automatic damage).
Paladin Turn 2: The paladin begins this turn still challenging Orc A. He thens spends this turn completely ignoring Orc A. He ends this turn by using Divine Challenge on Orc B (whom he has also been completely ignoring). If we allow the explotive interpretation of "or challenge a different target", then the paladin has fully satisfied this requirement.
Orc B Turn 2: Orc B is in the same situation that Orc A previously was. He either moves to the paladin who has been ignoring him or wastes his turn doing virtually notihing.
Paladin Turn 3: The paladin begins this turn still challenging Orc B. He then spends this turn completely ignoring Orc B. He ends this turn by using Divine Challenge on Orc C.
Repeat.
Long story short: The paladin must engage a target on the
same turn he challenges that target or the challenge will end and he will lose use of Divine Challenge for a turn.