Is it a problem if the frame of the house extends 1 – 2″ from the slab

It's possible the water is getting around your shower, possibly where the tile meets the tub or pan (if you have one), or behind the fixtures, or even around the door (if any).

I would check all of these and recaulk where appropriate before going in for wholesale destruction. Try splashing water by hand/bucket on areas you might suspect and see if that leads to leaks.

Or maybe you even have leaky plumbing in the wall. Do you have access to see in there?

If you don't have gutters and the grading around your house isn't sloped away, I'd start there. It's relatively cheap to do and will eliminate most problems. It's also nice, if you have a door at the bottom of a roof edge, to not enter under a waterfall.

Once you've done that (or if it's not possible to fix the grading) and the foundation is still wicking water, then an exterior water proofing system and french drain makes sense. This involves a painted on sealer, a free draining membrane that's attached to the wall (this gives a direct path for any moisture that reaches the wall to run directly down to the drainage pipe), and a perforated drainage pipe running around the perimeter of the foundation that drains well away from the house. If a system like this isn't installed during initial construction, it's often left to a last resort because of the expense and labor of removing any landscaping and soil that is against the foundation.