Iron and related commercial iron chelate herbicides work fair on dandelions. And hand pulling of weeds works if you don't mind the back-breaking labor. However, you might want to try a denser type of grass. Sod, if possible, if not...then repeated overseed following aeration. You need an athletic type of Kentucky bluegrass. A dense, highly rhizomatous cultivar would be more weed resistant.
A dense cultivar like Langara would be a good choice.