When any of us 'freeze at the helm' we have SIMPLY exceeded or skills envelope. In other words we have lost any reserve of options we may or may not have had in our back pocket.
In left handers hitting the front front brake can be a disaster as it will allow even more weight to transfer to the tip over line between the front and sidecar wheel This so called tip over line is the center of the radius that the bike will try to flip over the sidecar at when the rear wheel leaves the ground.
Hanging off with weight over the rear wheel as much as possible will help in the riders favor. If anyone has lifted the rear wheel of a rig in a turn away from the sidecar at speed they know it happens very quickly. It will either come back down to earth or keep on it's path. Hitting the front brake does not help it come back to earth as when the front forks compress more load is taken off the rear.
Right handers (turns toward the sidecar) seem to be the spooky thing for newbies. Left handers are the ones that newbies get brave in quickly but they can bite quickly and hard. Right handers are much more controllable once experience is gained. Lefties are controllable also but there are limits dictated by each outfit. For the most part we are talking about the dual sport /adventure type outfits here. High CoG, long suspension travel etc. is their nature and rightfully so. A jeep is not a corvette. Antiswaybars help a lot , good suspensions help also , track width helps but it may be a hindrance when off road. More lead helps but it has it's own drawbacks. Hanging off will help also but the traits in a left hand turn are still there only at a higher speed. Yep there are limits and finding them is half the challenge. Sneaking up on the limits of your own personal outfit is by far the safer way to reach them.
I shouldn't say this but breaking the rear wheel loose in left handers can be the key. This is not something that an inexperienced rider on a new machine should attempt as if it does hook up or if you hit a rut the wrong way the earth may suddenly be upside down for you.
Obviously terrain comes into play here a ton. Loose surfaces are much different than ones that provide good traction.