Dripping tub; polybutylene pipes

Note: My knowledge of plumbing is at novice to medium. I am at novice level, but can research if needed.

Tub was dripping a couple of months ago and a plumber came out and needed to look at the fixture behind the wall. However, because the builders of the house put the air duct between the wall behind the fixture and the fixture itself, there was no panel. So I had to rip out the tiles around the tub faucet and the control valve. (did quite a good job if I say so myself)

We have polybutylene pipes, so in the basement we have, what I believe is called, the manifold; a gray box with pipes sprouting from it and valves underneath each extension. The manifold has "cold" on the left side and "hot" on the right side.

The cold side turned off fine but when we turned off the valve for the hot side for the tub, the valve started leaking. At the time it wasn't such a big deal as the dripping stopped from the tub.

However, now the dripping in the tub faucet is dripping so fast that it is almost a constant stream. Also, when I turn off the valve for the hot water to the tub (the cold water valve for the tub was already off), the valve itself starts to leak a lot. So, I am torn at what exactly to do.

One of my questions is if I turn off the hot water valve to the tub and the leaking starts from the valve, what are the chances that the valve leakage will stop?

Another alternative is this: years ago when we first moved in to the house, the upstairs cold sink faucet was the cause of the ceiling dripping. Would a good alternative be to have the home warenty people come out and try to find the leak for the cold water sink and collect on the lawsuit to have all the polybutylene pipes replaced for free?

By leaking you are meaning into the tub from the spout right? What did the plumber do behind the wall, was there a leak in the wall? If not why would he have to open the wall? It sounds like you need a new cartridge and possible seats if its a 2 handle valve. It has nothing to do with the PB pipe.