Most green horses I've worked with will bolt when spooked, or shy away from things.. without an experienced rider to handle these reactions calmly and bring him back appropriately, it will just result in bad habits forming. Unless you can confidently walk, trot, and canter I would not recommend taking your green horse to a show. There is always a chance of something happening and unless he can be controlled and be brought back to a calm state afterwards... it just spells bad news to me. It's your responsibility to make sure your horse is ready for an experience such as a show for everyones safety.. your own, your horses', and all of the other competitors and their own horses as well. If your trainer does not think your horse is ready for this, then I think you should listen to them. If you don't have the experience to ride the horse yourself in a show, then I would only assume that you wouldn't have the experience to make that call.
For everyones safety, and to prevent bad habits from forming in a young horse.. I would listen to your trainer.