Hi pony,
Welcome to the Uni and our Forum!
Before I start finding an answer to your question, let me state that all horses are claustrofobic! This is part of their survival mechanism. In the wild horses need wide open spaces to feel comfortable, any restriction could mean a preditor has a better chance to attack. Your mare shows  a typical reaction of female horses, they defend their back-end, no stallion is allowed to touch that part, until she's ready for it...so a mare in heat finds herself sending away the stallion, until the only moment, when her hormones tell her it's right. Her reaction is a natural one. 
Does this mean there's nothing you can do? Not at all!!!
 

Please watch all videos on this Uni that help you understand the advantages of long-lining and the disadvantages of single-line-lungeing.
 
There's no limit to learning...and it's fun to deepen your knowledge every time you work with your pony!
As Monty says: it's important to have fun when training your horse, but more important is that your horse has fun!
Before we come to the desensitizing to the longlines, please make sure you have ruled out all other items!
Our forum is here to help you in every possible way to find your own path, don't hesitate to ask all questions that come up!
Please stay in touch!
Miriam  

Hi Pony

Welcome again, I'll just add a couple of questions to Miriam's post. 

Can I ask how long you've been involved with horses and is this mare your first horse you've training or have you started other horses before? 

Mel
x

Hi, I have never longe lined her before. I have only recently come across it. She is the first pony I have trained and I have a trainer that is familiar with natural horsemanship to help me but she can't come very often. I have desensitized her on both sides and she is tense on her off side but will not bolt. She only bolts when pressure is put on both sides. Maybe it is because she is unsure of what I want? Are there any exercises that I could do with her to help with this so I can start getting into riding? 

Hello Pony and welcome to the forum.  My thoughts on what you are presenting to us would be to back-up and slow yourself down a little.  All of us must initiate the training  young horse, no matter what our experience level may be, with a very slow, methodical and incremental approach.  This approach must be free of stress that would produce any thing close to putting the horse into the flight mode mentally.  The opposite of that is RELAXATION and that is where successful trainers do their best work.  

My suggestion to you, Pony, would be to develop a two-way relationship with your horse to build a trust level that would allow you to work on both sides of the horse with a calmness that is free from any anxiety and welcomed with trust.

One exercise that comes to mind that could bring this about is leading from behind.  This will be started in the round pen with you distributing 5 different piles of hay at various distances around the round pen.  This exercise is to be done at liberty with no tack on the horse.  It starts with you bringing the horse into the round pen and un- tacking .  Then you walk away and allow the horse to select the hay pile while you are standing back and away, possibly on the other side of the round pen.  Allow a few minutes to pass; then approach the horse from the rear and throw your head in an upward fashion while pointing with your right arm and hand[if your going to the right] and send the horse ahead to the next pile of hay..Don`t be afraid to stay the course until the horse has moved on [just stay out of the kicking zone]  This entire exercise will go on until all five piles of hay have been fed upon by the horse [probably should take about 30-45 minutes].  Then you would halter the horse and remove it from the round pen.  Wait two hours, then repeat the process.

With this exercise you are learning the language of equis as this is precisely the way that horses move each other around in a herd setting.  It demonstrates dominate behavior and leadership on your part, while the horse compiles with recessive behavior by offering the space that he is eating at, to you.  You then find yourself in the middle of a communication process that has gone on for millions of years.  You can build a meaningful trust through this procedure because once you think things through,because, so many aspects of being with a horse will have been accomplished.  I would urge you to try this  with your horse.  You will probably be surprised at the results.  Horse training is all about embracing a give and take relationship.

`Hope this helps you

Bud

P S. Pony:  In order to help you be seen on both sides of the horse, I would change the direction of the horse`s movement when you start a new session.  Horses seem to watch  you out of the eye relative to the direction that they are moving in. [right directed=right eye etc.]  As your skill level develops [should be commensurate with the horses`focus on what your asking of them], you will find yourself leaning toward the center of the round pen, which eventually blends itself into directing the horse from the back. to a little more on the side.  Now you have the beginnings of longing with a horse that is totally relaxed.

Please let us know about your progress

Bud