i've driven the ohio-florida trip many times, many ways!
i took my gram several times, my mom a few, and my mom and my kids (now 14 and 4yo). we always drive straight through, because i can't wait to get there, and i always do all of the driving.
it has taken us anywhere from 18-21 hours, depending on who is traveling. obviously, the kids lengthen the trip, because no one ever has to go to the bathroom at the same time, lol! i have traveled I75 (i think it was) through ky, tn, etc, and I95 route (through va, nc, sc, etc), and much prefer the latter. it doesn't seem as mountainous and you don't have to travel through the entire state of georgia, which seems to take forever! also, there are more frequent exits, for those bathroom stops!
we usually leave at 3am, so the kids can sleep, and make our first stop at beckley wv, which we're familiar with. after nightfall, we only stop at busy exits or travel centers and we stick together like glue. we have accidentally stopped at some pretty rough looking areas, but as long as you follow usual traveling safety tips (keep the car locked, stay together, stay in lighted areas, etc), you should be as safe as you would be traveling in your own area.
overall, i would say that it is a long trip (especially coming home), but it is better than not going at all! just keep your family together and your eyes and ears open!