Firstly, I don't think you can separate the double-skins without further damage.
If you want it to look really nice, buy a new one. If, however, a functional and decent looking repair is good enough, that can be done too.
Get a piece of ABS sheet from your local plastics supplier. It is cheap and the thin stuff bends and forms easily. Remove all the paint, down to the plastic, on the damaged bottom of that case and cut a patch from your new sheet. Tape the patch onto the bottom, and use a heat gun to allow it to form to the shape.
Use Methyl Ethyl Ketone ($10 per quart, home depot) to bond the patch to the base. Make sure the other painted sides are well taped, you do not want that solvent on them.
When that is done the entire bottom of the case should now have a new skin bonded to both the good and broken parts. You can then finish it any way you like. Truck bed liner on the bottom would work, and it is hidden from view most of the time.
If that doesn't work, or if you make a mess of it, you have spent about $15 ... buy a new one.