This Ice Cream spot is one of my favorites!
They will accommodate your children, and give them a "half-kiddie" cone (Which is a reasonable scoop of ice cream), and their regular cones are... a lot of ice cream!
One of the main attractions (besides their own, made on the premises, ice cream... try the coconut, banana, and reeses PB cup) for our family is the location. Unlike a number of the other roadside ice cream spots, Carters has a more "bucolic" setting... with picnic benches against/among the trees, and away from the road. The view is lovely, with a farm on one side, and a view of Haverhill across the river from this Bradford location.