There is possibly more to this.
Does the vehicle drive ok without a caravan on?
Get a friend to help, rock the steering wheel back and forth (steering lock off). Which this is being done crawl under the front and look at all the ball joints and the pitman drop arm. You should be able to see and hear any worn parts. You can also look in from the bonnet too. Placing a finger/hand on the steering box will help you feel if there is slop in there. Also make sure it is actually bolted to the chassis, you'll see it moving if it isn't.
When a steering box wears or has lots of slop, you find you will end up counter steering, but feel like the wheels aren't fully responding to your input. However, I'd expect this to happen with or without a trailer on the back.
Other things to check are the suspension. The axles are attached to the chassis via rubber bushes. At the axle end and at the chassis end. Should these be worn or loose, then you'll get additional movement from the axles causing the vehicle to drive badly. But again, I'd expect this to happen under all driving conditions.
If it truly is only with the caravan on the back. What sort of hitch are you using? Are you using any kind of stabiliser bar or hitch system? What sort of nose weight are you seeing? How much is the back of the vehicle squatting?
Do you have a picture (side on) of the vehicle and caravan hitched? Excessive nose weight will make the front wheels go light when towing. A badly weighted trailer can also push the tow vehicle about.
