If the problem is just water getting out of the tub by running down the wall to the tub edge and then out the front of the tub there are products to fix this.
The make plastic flashing type of things that look like triangles that have adhesive on two edges. They stick to the wall and the tub and create a barrier for the water. You position these things on the front of the tub so that when the water runs up against them, it drains back into the tub.
You can find them at most hardwares or home supply stores. Sorry I can't remember the name of them but they do work and are rather inexpensive and not too obstrusive.