Hello, Christy --
I do have a suggestion for how to handle this situation in a courteous and gracious manner. And as a party planner with a children's etiquette business, I have a little bit of expertise to offer. :)
Please don't leave the bear in the child's cubby at school. Other children who were not invited to your daughter's party will see it and may feel sad that they were excluded from a really fun birthday party. Many schools have rules against doing this.
But a Thank-You Note is especially appropriate in this instance. I'm betting the mother of the child who had the tantrum at your party is feeling absolutely wretched right now. Who among us wants to be the mother of the child who misbehaves in public?!?!? She's probably wondering what on earth the other mothers think of her and of her parenting skills. She may even be wondering if removing the child was the right thing to do.
A gracious Thank-You Note from you, expressing your understanding, support and appreciation of her decision, would probably be a great relief to her. Simply say something along the lines of:
"Thank you so much for coming to Suzy's party at Build-a-Bear. We're sorry that Sally was unable to stay -- but please know that all of us who are mothers of young children understand that little girls sometimes have bad days! We very much appreciate the way you handled the situation. Our hats are off to you, for modeling good parenting!
Suzy just loved the (doll, game, gift) from Sally, and has been playing with it all weekend.
I'm wondering if we might make arrangements to get to Sally the bear that she picked out on Sunday? We did go ahead and stuff it for her. I'm reluctant to send it to school because other children might feel left out, but would love for Sally to have it."
Add your phone number at the bottom of the note so that the other mom will be able to reach you. If she does not want her daughter to have the bear (and I am guessing that she won't, especially if you take the convenience of a school exchange out of the equation) she won't follow up. But she will very much appreciate your kind offer, and your expression of support for her in a very embarassing social situation!
If the mom does want the bear, you might consider meeting her in the parking lot at school prior to the start of the school day or at the close of the school day. Or, if she lives at all near your neighborhood, you might agree to drop the the bear off on her front porch one evening.
G. B