First, I don't think you completely got rid of it. That happened to my GD also. She just kept getting it; finally I came to realize that we weren't completely getting rid of it.
Stop using the Rid and switch to Lice MD. When my GD had it continually for about a year, I switched up and ONE APPLICATION of Lice MD got rid of it. You should, and I did, follow-up with a second treatment in about 9 - 10 days but after the first application I never saw any more signs of her having it. The follow-up was done "just to be sure." Seriously, it's been 13 months and still no lice! Yahoo!
Like your household, no one else in the house ever got it. You say you don't bring the coats into the house, but lice can live for a bit of time without a host so I would either wash (if possible) or have those coats dry cleaned. Also, you need to put all stuffed animals and other things that can't be washed in a sealed garbage bag for at least 2 weeks. I left my GD's in the bag for a month just to be sure!
You do know that lice can't jump, hop, etc. They can only crawl. So, if she really was clear, she definitely put something on her head that was infected or she put her head close to someone else's head who was infected (close enough for the lice to walk from one head to another). She can't pick it up simply from being in a classroom with someone else who has it.
Also, blow dry her hair daily. The heat of the blow dryer and the force of the wind will knock any live lice out of her hair. The Lice MD will make her hair slick so that if there are any live boogers left in there, they can't attach the nits to her hair shaft because it's so slick so the life cycle will be broken. That's the trick - break the life cycle.
I do know how frustrating this can be, not to mention the damper it puts on your social life! But truly if you use the Lice MD, vacuum, wash, spray, blow dry, etc., you will get rid of it.