Re: cabinet refacing
It's really hard to get regular wood glue as such to adhere to laminate. I'd likely use a contact adhesive, and 5/8" 18 ga. brads to hold it. A goodly number of wood screw-type clamps will also be handy.
While yellow glue may eventually dry, it's going to absorb all of the water content into the back side of your 1/4" stock, which is going to make it cup. I would avoid anything that was water-based, which leaves liquid nails (not the water-based type), drywall adhesive, epoxy, alpha-cyanoacrylate (superglue), and contact cement as possibilities.
Remove not the ancient landmark, which your fathers have set.