Where is King Solomon when you need him?

I am struggling with the right thing to do is.  I think I know what I am going to do but it just doesn't feel right. 

Let me back up.  Laci got a doll from her grandma for Christmas last year.  She likes this doll but isn't super attached to it.  Occassionally she brings it to school.  We understand that with bringing toys to school, there is a risk of losing it.  A few weeks ago, a teacher from the school called me and said that her daughter lost her doll recently.  They looked everywhere for it and the last place they saw it was church (the daycare).  After seeing Laci's doll, she is convinced that Laci somehow ended up with her daughter's doll.  I explained that Laci had received that doll for Christmas.  I told her I would look out for a second doll at home in case Laci somehow picked up a doll at school and accidently brought it home.  I thought that was the end of it.

The teacher called me today.  She is convinced that the doll is her daughter's doll.  She explained again how attached her daughter was to her doll.  She offered to pay me for the doll so we could buy Laci a new one.  I have several issues with this.  One, why doesn't she buy her own daughter a new doll.  Maybe this could somehow be a lesson to her daughter about losing things and replacing them.  She also said that she isn't upset that Laci has the doll.  I was a bit offended by this in that I am sure it is Laci's doll.  This lady was practically in tears on the phone over the doll.  I will probably take her up on her offer.  Laci isn't very attached to it and it is a simple solution.  But it just doesn't feel right to me.  I feel like we are admitting guilt.  If it isn't Laci's doll, where is her doll?

Now I need to figure out how to "make the switch" with a new doll or explain to Laci why we have to give away her doll and get a new one.  I need to figure out a way to tell the teacher that we will give her the doll but that we are confident that the doll is Laci's.  Charlie doesn't want to hurt his mom's feelings by giving away the doll she gave her.  We have searched the house looking for the "missing" doll and didn't find anything.  Charlie spent time this afternoon looking at old pictures of Laci with the doll and matching up marks on the doll trying to prove it is Laci's doll. 

Sometimes it is hard to know what the right thing to do is.  I feel like this is the right thing to do.  At least it is the easiest solution with the least amount of conflict.  But it just doesn't feel right.

Last year, Laci's favorite story in her children's bible was King Solomon and the two mothers fighting over the baby.  She always asked to read the "fighting baby" story.  Tonight, Charlie joked that the solution is to clearly cut the doll in two.  I wonder what King Solomon's wisdom would be in this situation?