In the JSBsim file (eg: A320-231.xml) under the "YAW" channel, there are two Yaw Damper values.
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<pure_gain name="Yaw Damper Rate">
<input>velocities/r-rad_sec</input>
<gain>2</gain>
</pure_gain>
The value velocities/r-rad_sec is the speed of the wind in radians/second
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<pure_gain name="Yaw Damper Beta">
<input>aero/beta-rad</input>
<gain>-5</gain>
</pure_gain>
This is the direction of the wind against the body of the airframe, in radians.
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<summer name="Yaw Trim Sum">
<input>fcs/rudder-cmd-norm</input>
<input>fcs/yaw-trim-cmd-norm</input>
<clipto>
<min>-1</min>
<max>1</max>
</clipto>
</summer>
This add together the rudder controls (from the pedals) and the rudder trim control, then ensures it's in a range -1 to 1
We then add all three of the above together, and ensure it's in a range of -1 to 1 and output the value as "fcs/rudder-sum"
Then the rudder-sum value is converted from degrees to radians and output to "fcs/rudder-pos-rad"
Then the JSBsim C++ code takes the fcs/rudder-pos-rad and outputs fcs/rudder-pos-deg somehow.
Finally we take the fcs/rudder-pos-deg value and normalise it from -25 to 25 down to -1 to 1 and output as fcs/rudder-pos-norm
So a bit of tweaking of the Yaw Damper Rate gain value I think could be the first place to tone-down the effect it has, a bit of playing around with a value of 0.5, and a value of -1.5 used in Yaw Damper Beta should help keep you on the centreline during some strong crosswind.
Hope that helps
S.