If you fill the tub and let it sit for 10 min., then drain it, will it leak then? If so the problem is in the drain, maybe gasket to tub, or first glue joint. And if not, chances are high you will have to open wall and repair mixing valve or the pipe from there to shower head. What is on the wall behind shower head, hopefully a closet

Hopefully it is the drain, since it sounds like theres already some ceiling repair in the kitchen. Good luck, let us know what you find.....