Your trainer should be teaching you how to ride and train your horse on the flat before even thinking about fences.
Your horse sounds way too green to be ready to start over even small fences. First, make sure the horse has no mouth problems. A bad tooth can cause a LOT of resistance to rein pressure. Then, after this has been checked, this horse needs more training.
A horse needs to be trained to 'follow its nose'. This is accomplished by using leg pressure and a shortened rein. The rein is shortened until the rider can barely see the corner of the horse's inside eye -- no more 'pull' than that. Then, the rider needs to 'push' the horse, using outside leg, into following its nose -- not pulling harder.
The horse must be taught to 'bend' around the rider's inside leg or it will drop a shoulder and not guide properly. The reins only determine what direction the horse's nose is pointed toward. The skill the rider has using his or her legs determines the position of the horse's shoulders, ribs and hind end. A rider must have control of all of the horse's body parts on the flat before the horse can be properly taught to go where the rider wants it to without resistance.
A horse must stay between a rider's legs and between the reins and go exactly where the rider asks it to. If a horse cannot trot and canter nice round circles and canter straight lines without pulling or pushing against the rider's legs on one side more than the other, the horse is not 'guiding' well enough to go on to more difficult tasks. A horse must be easily guided to the center of cavaletti poles and through and around markers before even thinking about small fences.