The best way to do this to avoid any problems in the future in my opinion would be to rip out all of the old tile and replace with new. To do this you could either replace the tub or keep the old one, if it is in good shape, hang what is called an MR (moisture resistant) drywall, or you can hang what is called a masonary backing for tile. It comes in 3 ft. by 5 ft. sheets. This can be screwed to the existing frame work and it makes a solid backing for tile work. Or, you could buy at any Home Depot or Lowe's what is called a shower body insert. It comes in three or five parts. You will still need to rip out the tile and put up the MR drywall boards prior to installing the shower body. Purchase with the shower body adhesive, utility knife, caulking gun and tub and shower caulk, to waterproof the job. This is only a fraction of ideas that can be applied to your problem. We purchased our home three years ago and had a similar problem. Our tile in the shower was black and gold. A real Pittsburgh Steelers fan color. It was horrible. We tore down all of the tile, and replaced it with the shower body. What a difference it made. It looks like an entirely new bathroom. If you should have any further questions, feel free to e-mail me directly, for I am a contractor myself. Hope this will be of some help.