I have no idea what that extra valve you describe is or is for, but I can tell you why your T/P valve on the water heater is leaking. You need a thermal expansion tank in the cold water line. The pressure regulator valve on the supply line has a check valve built into it. When the water heater heats, this causes the water in the tank to expand. In homes with no pressure regulator, this expansion is absorbed by the city water main. but in your case, the PRV stops this from happening. This build pressure in you water heater to the point that it trips the T/P valve. A thermal expansion tank absorbs this expansion. Perhaps one of the professional plumbers can identify that other "valve" or whatever it is, but I tend to think it can be eliminated.