It is very frightening. As there is nothing you can do, just take foot off throttle and let it sort itself out, some peeps make it worse by trying to steer out it don't happen, don't brake as that can make snaking worse..

You are more at risk of snaking while traveling down steep hills as the trailer is pushing the car.. One reason why they say to select a lower gear when going down hill...

We've had it happen a few times. Only mildly though.
It's not me that tow's mind. As both me and my other half are too young to have it on our licences I only put her through the test, my theory being if I'm shattered from racing do not want a few hour drive home.

For us, cruise control makes it nearly instantly snake. Never had it bad enough to move lanes though, so I wouldn't class it as bad as yours.
Don't fancy writing an uninsured race car off that's worth 10x as much as the disco. I suppose things will change with experience though, as before this season I drove the car to events and back, so we've not got a huge amount of experience at it.