You do not need to replace the valve. The tub spout has the diverter built into itself. Mixed hot and cold water from the valve will go down into the tub spout until you pull up the diverter knob on the tub spout which blocks the water flow and forces the water to exit through the shower head.

The tub spout is entirely separate from the valve. The 3 holes you see in the valve are the inlet ports for the hot and cold water and the exit port from the valve for the hot and cold "mixed" water. If you are going to replace the valve it is the entire thing you replace. All the way to the 1/2" threaded copper pipes that go into each of the 4 sides of the valve.

If you do not plan on replacing the valve then the next steps would be to repair the line to the tub spout. Then make sure you can find replacement trims for the valve- unless you are going to reuse the old trims in which case you are all good.

If I'm not mistaken, you can pull down with some force on the bottom of the spout.

If you turn the water on and do that, the water will come out of the shower head until you turn the water off (or until the pressure is low enough).

Sounds like the washers/gaskets on the valve have gone bad, you'll have to either replace the washer or the entire valve (if you can find a replacement).

Here is what the valve may have looked like when it was new (just to give you an idea of what you're dealing with).

Removal

• Turn off the water to the shower faucet using either a local shutoff valve or the main water valve for the house.

• Turn the shower’s hot and cold water all the way on, to drain leftover water from the pipes.

• Pry the cap out of the center of the diverter’s handle.

• Remove the screw in the middle of the handle, and then pull the handle off the faucet.

• Unscrew the metal sleeve that sits over the valve stem.

• Insert a Shower Valve Socket Wrench over the valve stem and turn the dirervter anti-clockwise to remove it.

• Replace the washer, or the whole diverter if you can find a replacement.

• Apply some Silicone grease (plumbers grease) to the washer before replacing the diverter.

Installation

Installation is the reverse of removal.

• Insert a Shower Valve Socket Wrench over the valve stem and turn the dirervter clockwise to install it.
• Screw on the metal sleeve that sits over the valve stem.
• Push the handle on the faucet, then replace the screw in the middle of the handle.
• Push the cap into of the center of the diverter’s handle.
• Turn the shower’s hot and cold water all the way off.
• Turn on the water to the shower faucet using either a local shutoff valve or the main water valve for the house.