Battery Charger using a buck converter
Lead Acid cells have a very low internal resistance. So a LA Battery discharged to 9 V will behave as a 9 V voltage source with a low value resistor in series. So that is why you measure 9V at the output when you connect the discharged battery.

What happens in a "proper" LA battery charger is that it enters current limiting mode which means that is will charge the battery with a predetermined current for example 1 A untill the battery is sufficiently charged. Then the voltage limiting charging will occur.

I see no current limiting measures in your schematic. This is BAD I would never design a battery charger without current limiting. Especially for a switching converter where the inductor can saturate and currents can become exceptionally large.

It can be that the current limiting is in the 18 V supply. Possible but not so elegant. There are plenty of designs that integrate voltage and current limiting in one solution.

Oh that IR2111 is only a driver ! Geez, I expected it to be a proper SMPS chip. So you're just PWM controlling the MOSFET from a microcontroller ? Please consider implementing a proper switched more converter with voltage feedback and all. This is not a design that I would build.

Some other remarks:

Usually temperature controlled charging is not needed unless the LA battery is in an environment which can be very hot or cold. For normal room temperature a maximum charging voltage of 13.6 - 13.8 V is usually all you need.

Discharging a 12 V LA battery to 9 V is not good for the battery, the lower the voltage the more chance you have to permanently damage the battery (sulfite on the plates). I would not go below 11 V to keep the battery in good shape.