I'm a day late and a dollar short, but since these are your husband's kids and you're blending the family, it should be a piece of cake.
I cleaned like a maniac for our adoption home study, only to find that the social worker who came over had rheumatoid arthritis. She leaned on her cane, stood at the bottom of the stairs and pointed to the rooms to make sure she knew which was which, and then sat on the couch and just chatted the rest of the time.
Cleanliness is great, but what they are looking for is really gross stuff, like you see on the news when people get arrested and their houses are condemned. Also, if you already have a relationship with-this person, they'll give you tips like, "You will have to add another screw to that railing so it's secure," but it won't prevent you from "passing" the home study.
Try to relax. (Easier said than done, I know.)