We have water leaking out from between the stem and bonnet nut on our hot watter handle in the shower. We tried to replace the whole thing but the old seat is stuck in a stripped. We bought the tool (L shaped thing) to remove it but it will will not come out. If we leave the old one in and replace the stem it still leaks between the stem and bonnet nut.

Any Suggestions?

Also, What the heck does the Bonnet nut do?

The bonnet nut compress the packing around the stem to prevent leaking around the stem. The seat is the surface that the washer presses against to stop the water flow. There are different size seats and different shapes. Some require a hex shaped wrench, some require a square tapered wrench. Shine a flash light in the stem hole and look at the shape of the hole in the center of the seat. If is is square you will need a tapered seat wrench.

Thanks so much! The hex one worked (after a good bit of tugging).
It is great to have my water back on! :)

Yes, but still... seat and bonnet nut are two completely different things. Replacing seat will not fix leak from bonnet nut.

For that bonnet packing leak. Open the valve so that it begins to lek past the stem.
Now just snug the packing nut up until the leak stops. CAREFUL! Don't over tighten.
Good luck, Tom