as him/her just what kind of a problem? A P trap is not a complicated peice of engineering marvel, its just a 180 degree bend in the pipe to keep out foul smells and to collect diamond rings when they fall.
Now, if the p trap is cast iron or clay and it has actually disengrated, then he/she is right, you have to go under and replace. But, now days they have cameras that can go on the end of roto snakes that will show you and the plumber what is going on with the inside of the pipes. I would find a plumber that uses this technique and have it done on your pipes and ask to see the monitor.
Get three more bids and ask each one if they have the camera. Ask what is the problem with my p trap? Pin them down with questions and don't be afraid to challenge them and do not be afraid that you might ask a dumb question. Its your money and before I would spend $1500 I would want some good answers.
Don't do anything until your satisfied. Now, you might want to discontinue using that shower until this is fixed, because if something is really wrong, continued use might make things worse. If that is the only shower, then go ahead.