Bathtub water is damaging adjacent wall

I have what appears to be one of those 4 piece bathtubs that comes in pieces. There is a back wall, the two sides and the actual tub. I have a persistent problem where on the wall opposite the side of the tub with the shower head it keeps getting soggy. The sheetrock continues to bubble and get damaged. It is happening where the bathtub meets the wall. The wall gets very spongy and soggy to the touch. I've painted over it more than once. I didn't build the house, so I don't know what was done and what sheetrock is under there.
You can see good pictures at:
http://www.greg-n-jen.com/bathtub/

The pictures don't really show the severity of how much its making the wall soggy and the bubbling up of the sheetrock, but you can see at least the area being affected.

I have two questions that I've been trying to find an answer to:
1. Is there something I can do/should be doing to keep water from damaging this wall? I assume its getting on the back of the tub and just following the groove between the side wall and the tub and getting into the sheetrock behind it and damaging it. I'm using a good fan in the bathroom and always let it run. No other areas are damaged including the wall adjacent to the front of the tub where the shower head is, where it presumably gets even more wet.
2. With these modular multiple piece tubs, am I supposed to be caulking those joints? Look at the pictures and you can see that I keep getting pink and black mold on the mildew resistant caulk.
Are these joints where the tub and back and side walls meet supposed to be caulked or should I pull it out of there? I don't know if those are made to overlap so it won't ruin the wall behind it, or if I'm supposed to keep it sealed up. It gets aggrevating cleaning that mold all the time.

Here is one sample picture of the damage, you can see more at my link above:


Thanks!
Greg

First, I'd take a level and see if the tub is level both from front to back and side to side. If not, then there's probably no way to keep water from dripping out. It appears you are using a shower curtain, since there's no door there. On many designs, the panels snap together with a flange, so if the walls are straight (not common!) then it is waterproof (but still needs to be level).

Once drywall has become wet, it really should be replaced. If moisture has gotten back into the stud wall and floor behind, there could be a lot of rot. I think you should pull a bit off and look once you figure out the leak. Not knowing how yours went together, if the tub/wall joint is well caulked, it may just be running out the side. I think you'd have to be there to really tell.

That's pretty typical on the outside of a tub.
That's why I like to have "legs" in front to the tub, down to the floor. I don't think anything looks bad with what you have, it's just that water will run down the outside of the tub and get the wall wet.

It's a bit hokey, but I have seen a few homes where someone ran a short bead of clear silicone along the top corners of the tub deck to channel the water back towards the inside of the tub so it wouldn't run outward.