So let me get this straight...
You just brought back a book that your kids checked out which is 55 days overdue. And you've now explained to me that the reason it was 55 days overdue is because the last time you returned books for your kids, eight weeks ago, you thought you'd brought all of the books back because you had counted them and saw that there were five of them, which was the number of books you knew your kids had checked out. However, as you've now also indicated, the reason there were five books in the stack, yet NOT the overdue book you've just returned, is because one of those five books actually belonged to one of your kids and not to the library. And now you've explained to me that your kids would really, really like to have that book of theirs back.
This I can understand and, indeed, sympathize with.
Unfortunately, you've also now explained that neither you nor your kids have ANY IDEA WHATSOEVER as to the identity of the book you mistakenly returned. You don't know the title, the author, nor even what it looked like. Compounding the embarrassing nature of this mistake is your now stated assumption that we've somehow been holding this mystery book for you here at the circ desk for the past EIGHT WEEKS. That we might have, as is our policy, assumed the book to have been a donation and put it into storage for our book sale or even added it to our collection is not a possibility that you have entertained.
I am even further astounded at your additional suggestion that we should now allow you to go downstairs to the storage room and have a look around for your beloved mystery tome. A nice idea in theory, but not very practical. For you see there are literally thousands of books in our storage area, most of which are not even divided into any sort of classification, some of which are not even in boxes but instead are kept in precariously teetering piles. And now that I have explained that to you I have been afforded the small pleasure of seeing your face fall as you realize the full extent of your folly. Because as much as you might want your mystery book back, the amount of work it would take to actually locate it, assuming it's even downstairs at all, has considerably lessened the intensity of your need for its return. Wisely, you have chosen to drop the matter entirely, at least until our mid-summer book sale, when you'll perhaps have a fighting chance of locating it again, provided you come early enough.
Oh, and by the way, that'll be $2.75 for the fine, please.
Yours in sweetness and light