I have a copy of "MANUAL for the Design of HOLLOW CORE SLABS" 2nd Edition, by Precast/Prestressed Concrete Institute. I receive it, upon request several years ago, from a sales rep at Spancrete, the major precast supplier in Wisconsin.
Chapter 4 discusses Diaphragm Action with Hollow Core Slabs. I have not used it as I seldom have to deal with this specific application, therefore I cannot offer detailed insight for you. The point in that this or a more recent edition of this manual should be available either through the PCI themselves, or from a local precast rep.
Typically, when I do have a lateral load necessary to transfer through precast material of any kind, I furnish the details to transfer the load into the precast along with the magnitude of the load on the construction documents, and then the precast engineer will design the precast to absorb and transfer the lateral load.
Is this typical practice in other areas?