Appears that we need to tighten the hot/cold water inlets to the shower faucet, but can't seem to figure out how to remove the shower faucet so we can get to the back of it - does anybody know the secret?
yep, there should be a white access panel in the wall behind your shower with 4 screws in it. Remove it to access the plumbing to your shower. If there isn't a panel you will need to use a hand saw or dremel to cut a square opening large enough to get your hands inside and then buy a cover to put over it.
I once had a similar problem. Thing was the shower handle was on a outside wall and there was no possible way to get at the back of it. I had to cut a access hole in the shower wall above the handle and reach in and down to get at it. I then patched the hole with some glass board that I had carefully caulked around the back side of first. It didn't look really perty but, it never leaked as far as I could tell.