Elaine, Home Depot seems to have "chicken wire" 2' tall, 50' long, for under $9.00 --
http://www.homedepot.com/p/YAR...
so, you would need 4 of those ($36 or so), and should be able to devise a rudimentary "gate" relatively easily; I'm more or less assuming the kids aren't there unless an adult or adults are present, who could open the "gate."
Of course, you'd also need some kind of posts to support the fencing -- HD has some 4' tall garden stakes for < $2.00, if you spaced them every 10 feet you'd need 20 of them, so that's another $40; but if you already have a picket fence around the garden, maybe you wouldn't need those at all, you could just fasten the chicken wire to the pickets.
Hope this is helpful -- I really applaud you for your efforts with the kids and gardening!