Hello Eli,
The schematic which you have included looks correct with the VEE pin connected to the SW node. The boot diode and the boot cap has been rightly placed between the VCC and VEE pins. You can use the LM5112 as a high side driver, provided you connect the VEE pin to the IN_REF pin externally. You also need to make sure that the input signal to the driver at the IN pin is referenced here to the VEE pin (switch node here) as well.
Thanks