Check the levers to see if they have throw adjustment screws. If they are there, they will be near where the cable enters the brake lever housing. Turning them in should move the lever closer to the handlebar, making it easier for little fingers to grasp. This will also mean you will need to adjust brake cable length.
Also, get a scotch brite pad and some alchohol and clean the rims where the pads contact the rim. Examine the brake pads for debris and glaze over. If they look glazed or shiny, rough them up with some a file or some sand paper. May consider installing better pads, like KoolStops, to increase braking power.
Good Luck.