You can apply a crabgrass pre-emergent in the spring when the forsythia blooms. Look for some products at your garden center and read the labels for when it's safe for children and pets to use the yard after application (probably a day or so). You'll likely find combinations of fertilizer and pre-emergents. Use something that is just pre-emergent. You will not be able to sow grass seed until the fall if you use pre-emergent in the spring. Early fall is the best time to sow cool season grasses like fescues and KBG.

If you are digging up and starting over that indicates that you are also going to reseed your grass. Preventing crabgrass seeds from taking over your lawn with herbicide means preventing your grass seeds from developing right along with it.
Unless you use and expensive herbicide that kills crab seeds and leaves your grass seeds alone.
Why not just put down sod since it is a small area and the kids don't have to breathe in the herbicide from the dust.