In replacing the water diverter stem (that the tip was broken off) of a two handled faucet tub faucet, after many attempts of placing it back on... The hot water keeps coming out the tub spout. I've tightened and tightened it back in and it seems useless. So, I have to cut off the hot water supply until I'm ready to use the bath. Otherwise, I can't run any hot water for anything. What did I do wrong?

It sounds like you have a faulty seat. To check turn the water off and open up the valve. Feel the seat. If it has nicks or rough spots then the seat's bad. Some seats are replaceable and some are built into the valve body. If it's replaceable you can unscrew it and purchase a new seat. If it's built in you'[re looking at replacement unless you can find a old timey plumber with a reseating tool. Good luck, Tom

two handled faucet tub faucet,

So, I have to cut off the hot water supply until I'm ready to use the bath.

Those statements make me believe you are talking about the hot water stem, not the diverter valve

Make sure that the stem is in the open position (turned all the way counter clock wise) before reinstalling. If the stem is in the closed position the stem will hit the seat before you have the body screwed all the way in. If the body is not installed all the way in the stem will not press against the seat when you try to turn the water off.