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So, wie du's schreibst, ist es richtig, aber man würde dich auch ohne das "between each other" verstehen.
Du könntest auch sagen please stand slightly apart to keep those behind you in the picture, aber das war ja nicht deine Frage.
Und ja, distance klingt komisch, entweder zu distanziert oder zu technisch.
leave some space is a correct, idiomatic phrase in itself, but trying to use each other like that is wrong. It's difficult for me to think of an idiomatic way to express what you want to say using the leave some space phrase, so I would rephrase the first part of the sentence as reverend has done, and write Please stand slightly apart [from one another] to make sure everyone's visible in the photo. The bit in [ ] is optional.
Note that I prefer your (delia87's) version of the second part of the sentence not because reverend's version is wrong, but because (1) yours sounds less formal and (2) to avoid the use of to keep s.o. in the picture, a phrase which is usually used metaphorically (meaning to keep them informed).
I'd probably say:
Space yourselves out a bit so I/we can see everyone.