I purchased a home a year ago and we discovered a leak when the first floor ceiling developed heavy water stains. We also noticed the water had traveled down a wall into the basement ceiling. We stopped using that shower immediately, and had a plumber come in. The plumber detected no leaks and said he believed it to be water flowing off the back of the tub onto the floor and leaking through. We used the tub with no leaks for the past year. We recently had a shower door installed and the caulk and grout replaced, and began using the shower again. We watched carefully but saw no water the first couple days and thought this was fixed, but now it is clearly still leaking as there are new water stains on both the first floor and basement ceilings.
What could be causing this leak, and more importantly, I'm certain with that much moisture there has to be mold - if I have mold on multiple stories between the floor and ceiling and between the walls - can this be corrected (and at what cost?) or will the whole house basically need destroyed?

Is the shower on an outside or inside wall?
When the plumber 'detected no leaks' what did he do, exactly?
Am I correct in that during the time there were no leaks, you didn't use the shower, just the tub?
My first guess is that there is a leak on the way to the shower head. I would run the shower full blast for 10 minutes and go downstairs and in the basement for the next hour or so to see what might be leaking, and report back.

Just because the ceiling downstairs might be under the back of the tub doesn't mean water didn't run along the ceiling to a low spot and settle there.

Most mold isn't toxic, it just can cause congestion and irritation to mucous membranes. Toxic mold scares are really very rare and the whole thing has been blown out of proportion.

You certainly don't have to nuke the house. You can let it dry out on it's own, scrub with bleach what you can reach, or rip out what you want.

Have you ever pinned it down as to exactly what is being used that causes the leak? It could be a drain but that would leak every single time you use the tub. It could be a supply but that's also pretty much 24/7. Or maybe it only leaks when you use the shower diverter in the tub. You got mold no doubt and it will not be easy or cheap to cure that issue. Get 3 bids from abatement outfits and listen to what they think must be done, then decide if you think it's a DIY project or not.

I agree with ballengerb1's expertise on the plumbing and forgot about the diverter.
I just want to say that a mold abatement company is going to want your business and I'll bet all of them will tell you it's urgent and so on. They wear moon suits and set up fans and vast amounts of plastic and it's expensive.
It isn't so much the type of mold, although that's what they might tell you.
For mold to be a real health hazard it has to be
- in very high concentrations
- you have to be exposed to it for a long time
- you have to be immunosuppressed
A leak can dry out and the molds die. When you should rip it all out is when it's foundation or gutters or flashing down the inside of walls.