I do not have children, but I think that a 'from scratch' campaign setting should take around 12-20 hours to be ready to run, and with just 4 hours a week of further fleshing out as they go as well as preparing for the you can have a top notch campaign.
However, giving you simply that time frame without at least pointing you towards methods and tools for being able to put something together within that time frame is...kinda useless. I would suggest that you begin by listing 5-7 Major Powers/Players in your world, and how they relate to each other. Has any gone through major changes in the recent past? Has their relations with another nation wildly swung in one direction or another? Then start placing those powers on a simple sketched map, and then give some really brief thought into the surrounding locales of each power.
Then, place a few parts of your world which have no 'major powers', some wilderness or wasteland or something. Add some secrets/histories to those places. Again, you don't need depth at this point, you need just seeds of ideas here. Rough outlines.
Add more powers and areas to taste. Through this process you probably have gotten some neat ideas for interesting interactions between the powers...some thoughts of ways an adventuring party would Hook into these should be given. The last bit you need to focus on is a 'starting locale'...do the same process but on a micro scale. Who are the major players and powers in the local area? Instead of nations or kingdoms or gods, it should probably be individuals and small groups. What are some areas nearby that no one has influence over? What sort of secrets lie there? Note where there is potential conflict between the local powers. Think of ways that an adventuring party might be drawn into their shenanigans.
Again, this won't take terribly long...though it might the first time around. The trick is not to let yourself dive down any rabbit holes and start listing the entire 10,000 year lineage of the King of the Fancy Elves or something. With practice, you can have a world set and ready to go in a weekend. The first time will take longer, around 20 hours.
Good luck!