With two or three days to get from Washington DC to Kansas City in February, I'd suggest that you plan on taking two days and driving fairly directly between the two cities. If it snows and you are uncomfortable driving in such weather, then you will have that extra day to just stay in a motel until the weather clears and the roads have been plowed. The 'I-68/I-70' route (actually I-270/I-70/I-68/I-79/I-70) is the shortest route using all Interstate highways. Those are the roads that are kept the clearest in the event of bad weather. It is also a fairly scenic route, especially between Washington and southern Ohio. If all goes well, you should plan on staying overnight around Richmond IN. Two days won't give you time for any major stops, unless you use that third day for sight-seeing rather than visiting with your family, but you can and should take time for some short stops each day to take a break from driving.