Slowing a horse down and exposure to showing?

I've always seemed to have the issue of slow horses for lessons. My personal pony, Juliet is almost the polar opposite. She's lazy at the walk, but will speed it up if you really ask. However, I can usually never get a decent trot out of her, it's always really fast and I try to half-halt and slow her but it doesn't work. She's the same at the canter and will break into a gallop if you don't half-halt about halfway across the arena. I want to start showing her but I know I need to slow her down some before I can compete in hunters. Any exercise, tips, advice on doing so?

Which brings me to my next point. Juliet use to do 4h shows (or so I was told.) but I board at a very small facility. I was the only one who really ever does much riding, I can count the times I've had to share the arena on one hand in two, almost 3 years. So, I'm not really sure how well she would do in a ring with 15 other horses. I take lessons 2x a week at the barn next door so I can ride in a group. I was wondering how I could get her more into working with a larger group. (I'm the only one who rides except for the amazing show jumper but, I'd rather stay out of her and her 17hh mare's way while they're jumping 4'6 and I'm doing groundwork on my 13.3hh pony.).
Also, may I mention that Juliet is afraid of her own shadow. I have tried despooking her and it doesn't work. I have had this horse almost gallop over a cliff because a clearly visible bunny scared her. So advice on helping her get over her fear of everything would also be nice!

You say you have tried 'despooking' her, but it didn't work - what method, specifically, did you use? Knowing what hasn't worked will help guide suggestions that may work.
As for exposure - start looking for horse events in your area and take her to observe them. Just being at a show/gathering/etc with the crowds, horses and activities can be a great learning experience.

I tried to expose her to things she's afraid of, it has partially worked, like she used to be deathly afraid of bikes, now she's still a bit wary but she won't gallop at the site of them. Juliet will spook at a jump she's been over a 100 times if you face it the other way, and I'm not kidding. She did this two days ago and it wasn't the first time.
She's my second horse, but my first horse was and still is a saint. She's 34 and I don't think I have ever seen her spook in the 11 years I've ridden her.

I can't give you much advice when it comes to spooking, but I do know a lot about fast horses.

You want to get your pony behaving from the moment you get on her back. Speak to her softly and gently tug the reins while warming up at the walk until she is paying attention to you. Watch her ears. If she is listening to you, in the least, she should have one or both ears flicked back.

When you ask her to trot, use a very light aid. Simply flex your calf muscles or squeeze gently until she breaks into a trot. Keep yourself calm and relaxed; she can sense your emotions. Check to make sure she's still paying attention to you. Also, make sure you practice circles, serpentines, and figure 8's. Bending will help your pony listen to you and focus on turns instead of simply rushing around to outside of the arena.

When controlling the pace at a trot, it isn't only about half-halts. It's about your seat and your posting. If you slow down the speed of your posting, she will slow slightly to match it. Keep your shoulders tall and square and sit back. If you feel her getting out of hand, say 'whoooaaa' quietly and give a small half-halt. And again, do not just rush around the outside of the arena. Do lots and lots of circles, big and small, and control them. One excercise I find very effective is to ride in a circle at one end the arena, spiralling smaller and smaller each time and then spiralling back out.

Do not canter until you can keep a controlled trot. If your pony is rushing at a trot, she will rush at a canter. Wait until you have reached the desired pace. Once you are ready to prepare to canter, slow your pony to a walk. Encourage her to stretch her neck and relax for a minute or so. Then, pick up a nice easy trot. If it's not what you want, don't let her canter. Wait until the pace is relaxed and even. The transition should not just be a run into a canter.

At a canter, sit full seat. Half-halt in the corners. If she starts to get out of hand, pull her into a tight circle and give a firm but quick half-halt in the next corner. Resist the urge to lean into circles, and make sure your inside shoulder does not collapse. Circles, circles, cirlcles and tons of bending. Use your inside leg to encourage her to bend around turns.

When all else fails, if she completely takes off with you and refuses to stop, drive her into a small circle and then halt her directly infront of a wall. Never let her get away with it.

Good luck. I hope I was helpful.