As far as I-95 goes, if you're going on a weekday it seems actually better than the weekends. I drove down from home (near Baltimore) to Williamsburg, and we sat almost completely stopped for two hours just south of DC (the drive should take about 3.5 hours for me, but instead took over 6). That was Saturday, and going home wasn't much better and that was leaving Friday morning, so hit that area about midday Friday northbound.
I'd do some google search of the area and look at traffic - do it at about the time you'd be hitting that area to see if it looks pretty clear. Since you'll be there about 10:00 or later in the evening, maybe it's clear. It is out of the way to take 301 - but I did that with my friend (her house is that way) and there is no traffic. I am afraid of that bridge though!! It would be out of your way, but if there's traffic I'd do it.
I'm sure the kids will sleep the whole way! When we did the drive from here, we left about lunchtime (kids had preschool in the morning), and stopped every two hours to stretch, have a snack and potty break, and get more COFFEE (LOL) and by 8:00 the kids were sound asleep - two drivers and we just kept going and didn't stop till Orlando (that was not the original plan, but with sleeping kids it just felt easier to just keep going).
Good luck! I'm sure it's going to be FUN!