I will not mention about the D4s as I don't know anything about it. What I mention below is based on my work with both the D4 & D800 / D800E.
Well here are my recommendations.
With your budget you are able to get the 14-24mm, 24-70 & 70-200mm & a camera body with some spare change.
Get the D4 if you need to shoot events at a fast pace, high shutter speed under low light environment (high ISO), high frame rate and the huge buffer.
Get the D800 / D800E if you don't need the speed and high ISO performance. The D800 will do very well for family travel, portraits & scenery shots.
Both cameras have the same AF module, so AF performance is similar.
The image performance of the D4 and D800/D800E is very good, sensor dynamic range goes to the D800 at ISO 400 & below, sensor noise performance & detail retention goes to the D4 at ISO 6400 & above. The D800 / D800E retains detail better up to ISO6400 vs the D4.
The only draw back is the heft and the amount you will be packing for your travel. The weight of a D4 or D800 plus the 3 trinity lenses is quite heavy. It is no small matter to lug them around when travelling with a family.
I always pack a D5100 when I travel with my family. When I am travelling alone for work I will lug the D4 with a back pack.