Roads no problem, apart from Ethiopia is slow going (up, down, people and animals all over the roads, 200km a day is good going sometimes) and the northern part of Kenya is unsealed whichever way you go.
But the Aswan/WH ferry is not reliable at all at the moment, and getting a return visa for Sudan +could+ cause problems, so you should try to get a multiple entry before leaving Egypt etc.
Honestly though, don't bother, you will be driving most hours of the day for most your days, including through Ethiopia which is quite an annoying country to drive in, and I can't see if being much fun for anybody especially kids.
Just go to Sudan for 3 weeks, really nice people and plenty to do, or just fly to Nairobi and hire a car or something.
Africa needs less tourists in a hurry imho ;-p And you would always be in a hurry....
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