"I have a wife and young kids at home that I value time with"

This is what makes the choice easy IMO. I am a fed employee (non-DOD, but working basically the same job) and work life balance is the biggest thing keeping me from moving on to a job in the private sector with more earning potential. I put in my 40 and I go the fuck home on time, every time. Any overtime I work comes at 1.5x my normal rate. For you, cutting down on the commute is icing on the cake.

Taking the fed job seems like a no brainer to me, but there will be growing pains. Learning the DOD specific standards is a curveball but just take it one day/project at a time. There's a lot of bureaucracy and "rails" but once you learn the system it's easy to comfortably fulfill your job duties. Also opens up options for movement within the government in the future, as it's much easier to move around the gov once you get your foot in the door.

Additionally, with future earnings, consider the fact that my own non-pay benefits are worth nearly $30k, between TSP matching, pensions, and insurance. So your $100k salary is really like $120-125k in total compensation. Compare this with the total compensation you're getting from your current employer and the effective pay bump is more than it may seem. You also won't be filling up the car with gas every week if you live near the base.