He said he hit the bed and then they got infected?
It does seem unlikely he could cut himself that badly by hitting the bed. You don't believe him, you didn't react, good for you! Nothing to be gained by trying to get a different answer.
Yes, only the kids are your concern. Thank God you're enforcing the breathalyzer. Sorry I don't recall your kids' ages and hope they're old enough to call you if he drinks while he's with them?