In the majority of episodes set aboard the Enterprise Dee, the children were out of sight and out of mind. I think the Enterprise E also had children on board, they just weren't a part of the story.
I have to agree. The E was almost as large as the D so no reason why there wouldn't be children aboard.
Except for the peacful era TNG was in which allowed for the families on starships idea ended when the Borg destroyed 39 Starfleet ships and the Dominion kicked Starfleet's ass when they made first contact.
Seeing as the incidents pointed out the idiocy of that policy Starfleet probably abandoned it about the time it finally sunk in that they were a military organization.
I take T'Girl
's point on board. There's absolutely nothing to suggest that there aren't
families on the 1701-E, off-screen. Nothing to suggest it, but nothing to disprove it either.
'Voyager' obliterated the idea of there being families on the ship, a big deal was made out of Naomi Wildman. But the TNG features and DS9 never did (overtly).
So maybe the USS Voyager never had families on board, but that could be down to the size of the ship or the idea that it wasn't a "long range" space mission sort of vessel. Families might be outside her mission statement (which was probably shorter tour-of-duties anyway, so no-one needed
to bring their folks with them, if returning to base was always intended to be more frequent).
Indeed to your last point, Deep Space Nine was at the frontline
of the Dominion conflict, but nobody told Miles to send Keiko, Molly and Kirayoshi away. Which seems to indicate to me that the 'military families' concept begun with TNG was obviously still in play in that series.
So really, I'm gonna call B.S. on the whole "The Borg and the Dominion made Starfleet realize that having families around was a bad idea" theory.