How would you go about cleaning a lawn after a dog's been sick so kids can play on it again?

My dog has been violently ill for a few days (he's seen a vet and is being treated and getting better) and he's had diarrhea and vomitting all over my lawn. I have small kids who want to play out there, but obviously it's not clean right now. I'm trying to find out if there's any way to clean this mess up. I tried spraying "the splats" with the most forceful setting on the garden hose, but that's kinda just pushing it around I think, not cleaning it. I'd love to find a way to disinfect the lawn as well as remove the splats, but if you even have an idea just for cleaning it off I'm open to suggestions!