A couple of ideas, not sure any will work for you. I have two kids (4 and just about 3) and we drive from Raleigh to SW MA at least twice a year.
I do the overnight straight through (leave Raleigh/MA at 8-9PM, arrive next morning at 7-8 AM), letting the kids/wife sleep. I have done it in as little as 10 hours and as much as 19; drove back alone from MA to NC the Sunday after Thanksgiving last year.....got to NYC no problem and 99% of NJ was fine too. The last toll booth in NJ was all jacked up as they were working on the Delaware bridge. Basically from the end of the Jersey Turnpike through DC was one giant traffic jam. Realizing that isn't doable for you.
1. Take 287 over the TappenZee (or whatever the name of the new bridge is). You can stay on 287 around NYC and jump on the Jersey Turnpike around Edison NJ which allows you to skip NYC proper and the GW Bridge Toll (15-20 bucks last time I went over).
2. Time your travel around rush hour in DC. From Hartford DC is about 6.5 hours. Either hit DC around 2-3PM or wait long enough to hit it around 7-8PM.
3. If you can, I would rest after you get past DC. DC is a little more than halfway (I think B'More is technically halfway). But the traffic south of DC (more specifically Fredricksburg) is way less than North of it.
4. I would not recommend driving I-85 between Petersburg and Raleigh at night. Between the lack of lights, the poor sight lines with the trees along the highway, the remoteness and the construction/single lane travel from the VA-NC border to Raleigh, it really isn't all that fun.
5. If you are willing, there is a "Western Pass" that completely eliminates the NYC - DC stretch.
From Hartford you would go:
1. 91 to 95 to 287 (cross over TappenZee)
2. Get on I-78 W and stay on 78 til Harrisburg
3. Take state Route 15 south around Gettysburg
4. Stay on 15 through Frederick MD and remain on 15 until Opal MD (GPS would probably have you jump off 15 at I-270 in Frederick, but doing so puts you back on 495/395/95 NW of DC))
5. Jump on 17 in Opal MD.
6. 17 Dumps you on 95 S in Fredericksburg, which has added 100 Miles to your trip, but you missed Entirely NYC, NJ, B'More and DC and time wise, is basically identical (assuming normal traffic on 95 S).
The things to keep in mind with the Western Pass.
1. NE PA is pretty sketchy - gas stations with porn shops and trucker bars.
2. More Semi-Trucks on this route but way less traffic.
3. Snow is more an issue going this way, so check the weather.
EDIT TO ADD - The Western Pass I use. You can also do the I-81 version; but I chose not to simply because it puts you that much further West.
https://goo.gl/maps/UeKwygcCqDS2