I have let a sick toddler finish the day because I knew she’d be in her contained playpen for nap, then straight outside (I disinfected during nap). So that part I understand.

I would put out a message/e-mail to all parents, as a reminder at the start of cold/flu season, and spell out your sick policy including when they can’t come (when they’ll be refused or sent home), for how long, and what happens if they dose and drop.