I have FF in the form of a 5D and had K5 (now K30).
I also have to 2 small children.
Personally, I don't feel that I missed anything with my K5/K30 shots over the 5D.
The DOF can be shallower for the same FOV on FF, but a lot of shots needed more DOF especially indoors which meant stopping down on FF required a higher ISO.
FF can have better subject isolation thru that shallow dof and wide looking fov 'look', but not all shots require it.
Your 55/1.4 is also a far better lens than the kit lens for the D600 (though a cheap 2nd hand 50/1.8G would set you right too)
IMO, the 55/1.4 already gives you enough DOF control for most needs.
What I found most useful for my children/family shots indoors was a flash or two and the tenacity not to be too lazy to reach for the camera.
And shoot lots.
2 shots just taken over the weekend.