‘Between ourselves’ tests you on prepositions.
Prepositions are such handy and vital words ... yet speakers of various languages use them surprisingly differently.
In French, for instance, you would (quite logically) come in from 'under' the rain and get 'under' a warm shower, whereas in English we would more naturally say 'in from the rain (or 'out of the rain'), and into a shower'.
English also says 'between ourselves' (as does the French, 'entre nous'), while German idiomatically uses 'unter uns' ( = 'under us').
So you do have to watch carefully how English does such things!
Smiling 'for' the President is a fairly good alternative (Answer 2), but the remaining two Answers ~ though generally understandable ~ do not qualify as clear standard English.