No civilian families on the Enterprise-E. One of the reasons its smaller than the Enterprise-D.
Incorrect.
The reason the Ent-E is smaller is likely because new technologies allowed for the Sovereign class to be more compact while packing much more firepower compared to a Galaxy class.
It's a new design which is perfectly suitable for deep-space exploration.
Having said this, I don't think the Enterprise-E would ditch civilians/families.
If SF 'learned it's lesson with the ENT-D' then it should have learned it's lesson centuries earlier ...
To my knowledge, civilians and families were present in ships that came prior to the Enterprise-D in times when wars were fought and long exploratory assignments were handed out.
It would be likelier that the civilian personnel that cannot contribute to star-ship operations would be unloaded at the nearest star-base/planet in times of prolonged conflicts and/or wars.
For exploratory purposes (long missions) ... SF made a decision allowing their personnel to bring families on-board if the ship is big enough to accommodate them (the Sovereign class IS large enough).
This would hardly change after the Dominion War and conflicts with the Borg since the Feds had similar skirmishes and wars in the past with their neighbors.