Choosing resistor values to operate a Half Bridge Driver
The gate resistance is really the equivalent gate input resistance before the "capacitors" that make up the gate itself.



As such Rg really only comes into effect while switching and has no DC component.

When designing a mosfet driver the important thing is ensuring those capacitors are charged and discharged quickly while not overly stressing whatever is driving them. The IRS2003 has a minimum dead time of 400ns and so you need then to switch well within that number. 

The size of the resistor chosen can therefore not be too large.

It is difficult to tell from your schematic if PV+DWN is 12 or 18V. So I will assume 18V here. Derating the max output of the IRS2003 to say 250mA, with a voltage of ~18V when you pull down Q3 or Q4, that means you need a resistor of at least \$72\Omega\$

Obviously, if that rail is actually 12V you can scale that back appropriately.

Remember this current will only be required for charging and discharging the gate capacitances so its effect is short-lived provided you do not go overboard with the switching frequency.

However, it's prudent to actually do some tests with live components to verify the switching times are within the required window.