Oo I probably wrote the book on being nervous around horses! You're not alone, believe me. When I first started riding it took me a year and a half to even try a canter. And even today (and i've been riding for over 10 years) i'll still get nervous if my horse speeds up too much at the canter or trips. I also have issues with panic attacks about completely irrational things. Its taken years for me to get over and i've had more than one trainer give up on me.
Its also about finding the right horse to ride. I definitely support you going to the barn and spending time with the horses. That always helped me. Also, maybe you could arrange for a couple private lessons. Just you and the instructor to practice trotting without the added anxiety of having people around. That's how I was finally able to canter. Or you could even have your trainer hook your horse up to a lunge line. Then you can trot or canter at will without having to worry about the horse taking off or anything.