I’ve lived about 2 miles from the Lorton AT station for more than 20 years and have taken the AT a few times. Coming from NW Pennsylvania I would also recommend arriving a day early, especially traveling with four children, two of them small babies. The only thing predictable about traffic in this area is its unpredictable, but if you would be leaving your home at 9 or 10 PM the day before your AT trip, all roads *should* be clear sailing.
From Altoona to my home typically takes between 3 ½ to 4 hours in good traffic, if that helps.
All that said, leaving your home at 5AM and stopping for 1 hour to feed the babies would hypothetically get you here about noon based on the 5+ hours travel time you're allowing. Traffic on the Beltway and I-95 at that time *should* be moving along, but there are no guarantees that conditions will be perfect here or at any other point during your drive. If you're slowed down for any reason, that could push you into the 1 or 2 PM arrival time, at which point you would still make the cutoff time, but would likely miss early dinner reservations that you would probably want for your children. For that, it's best to check in at the AT station 11:30-noon.
There is a Comfort Inn on the opposite side of I-95 from the AT station and the distance between the two could be measured in yards (as in, maybe a bit more than the length of a football field), not miles. You get to the hotel by turning right on Lorton Road at the bottom of the I-95 exit ramp instead of turning left to go to the AT station.
Another option to consider is leaving at 9 or 10 PM, but stopping someplace like Frederick, MD (if you're taking I-270). It's a bit more than an hour from here, but you would get there earlier (maybe midnight-1AM?) so your family could get a bit more sleep, and it would give you a big head start to arrive in Lorton at a time you're comfortable with, although you would still have to navigate the Beltway and a few miles on I-95.
Hope this helps.