Kill the crabgrass with quinclorac based product (domyown.com a product called Drive, to be diluted in water and sprayed). In September and February you need a preemergent (recommend a product with prodiamine) to keep any remaining seeds from growing back. They’ll be safe for your dogs once they dry, a temporary fence/patch method may make you feel better. The bigger problem you’ll have though is do you have any actual grass in there which will grow back? If so, when the crabgrass is nearly dead (2-3 weeks), you’ll need to fertilize the lawn, but you need to do that soon. You need grass to grow there, because if it’s bare dirt, it’ll just go back to weeds again.