They way I read these statements, they will attend the same school/school district unless you both agree otherwise.  I'm not exactly sure why her attorney has chosen to use the language "primary placement."  I think, that unless a statement is made otherwise in the agreement, KTM may be on target that she is trying to gain the tax advantage.  You'll not really know what her intent is until it comes.  You can anticipate what her angle is, then just keep a very close eye.  She may think she is being sneaky, but you have us to help you.  Just bait the hook and watch her take it.  It probably will happen, but you will be ready.
I think you should go ahead and sign, knowing that if she tries to use this language to gain something in taxes, you can very easily take her back to court later and lower your child support accordingly.  The courts recognize the tax benefits of children, and if the parties are not equally sharing those benefits, an equivalent monthly credit or additional amount is assessed.
The idea is for you to get 95% of what you want in writing and start abiding by that agreement.  Once there is a new "status quo" a judge will be inclined to leave things as they are unless there is some kind of safety issue.