I'm very fond of Vittoria Randonneurs, have them on two of my bikes. (28 mm and 32 mm) Both sizes do fine on gravel (and dirt, and grass, and mud, and asphalt). No flats on either so far, and they are low pressure tires so they absorb some of the road noise.

From my own experience pulling my son in a trailer, I'd suggest the widest tires that fit on your rims. They help to cushion the bumps and rough stuff, so you don't transmit the vibrations and jerks to the kiddo behind you via the hitch.