Not sure if I am understanding you completely.
Why not infuse the whole thing in one shot. I have many times infused in my molds.
2 layers of 2x2 carbon twill, with 1/4 inch divinycel and 2 more carbon layers on top.
Fred 

Sounds good. Make sure you chamfer the edges of the foam. 

Wonderful info...thanks so much.

Whole aircraft and yachts have been built with nothing but thickened laminating epoxy for bonding, the filler being chosen depending on the mechanical requirements of the bonds.
Foam is pretty soft compared to cured resin, so a high strength bond isn't needed here, if something breaks it will be the foam anyway. Applying some "micro" (resin with lots of microballoons and maybe a little fumed silica) to the foam surface with a squeegee will fill the tiny bubbles and voids and provide an excellent mechanical bond to the foam exceeding the foams' strength and a good chemical bond to the laminating resin. Very lightweight, too, which doesn't matter here but might matter if the thing that you're building is supposed to fly.
If I can I try to avoid buying yet another resin which takes away room and will end up getting old on the shelf, try to do as much as possible with the least amount of different resins. Actually most work can be done with just one laminating resin (bought in bulk amounts) using different suitable hardeners and fillers, including infusion, wet layup and gluing things together.

12500cps is VERY high viscosity. Infusion specific resins have 150-400cps, the usual laminating resins 600-1000cps. The "150" should work, but it's not absolutely necessary.

As I understand it, ordinary laminating resin is too thin to achieve a good bond gap. The 150 looks like it would be fine. 

My buddy made the splitter out of 1/2" plywood and painted/sanded the top surface and applied epoxy to the bottom surface.
So West System laminating epoxy will not be sufficient to bond the divinicel to the backside (i.e. peel ply side) of the infused carbon fiber?
Hopefully this would work:

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http://www.uscomposites.com/epoxy.html

** The 150 Resin System is NOT recommended for the layup/laminating of fiberglass, carbon fiber or Kevlar. It is too thick and will not properly saturate the cloth. **150 Thick Epoxy Resin System is good for some types of bonding and coating appplications. The thick viscosity of this resin allows for high build and low sag. This resin can be combined with your choice of 4 different hardeners(see descriptions below). You can easily make an adhesive, putty or filler when combining the 150 Resin System with a product from our selection of powder fillers. This epoxy system will cure very rigid, for applications requiring good flex we recommend our #635 Thin Resin System.

Resin Viscosity: 12,500 cpsTables below show kits in which the 150 Thick Resin can be purchased.

Epoxy resins require a hardener to initiate curing which is included in the kit.

150 Thick Resin can be used with your choice of 4 different hardeners.

Your method will work fine. Just make sure you bond the divinycell to the first skin with a structural adhesive before you layup the reverse skin. Can use a proper epoxy adhesive, or just use add enough fumed silica to your laminating resin to make a nice thick paste. 

Gelcoat:

Hey guys. Just finished up this mold for a friend. The plan is to make a cf splitter with a divinicel core.