I agree that she wasn't born with the natural elasticity and suppleness of a warmblood, but she can still be soft and supple. That will come with time, proper training, conditioning and patience. Horses built with a short neck, thick throat latch and a short back have more of a challenge getting there but they can do it.
Here's an article that Dr. Thomas Ritter did for Dressage Today back in August of 2008. If I had the issue with me at work I would scan it in for you, but here's the article without pictures. There are some great exercises to help get you started. I had one of my biggest light bulb moments in my learning after reading this:
Right now I would concentrate on forward and riding her in a training level contact, not asking for a frame and doing most of your work in trot, walk/trot and trot/walk transistions. Focusing more on the quality than quantity of the transistions. If she was bred to trot than it would be understandable that she would have trouble cantering until she's stronger and more balanced.
It's hard to tell from the video but are you riding her in a mechanical hackamore? I would put her in a nice mild oval mouth loose ring snaffle. Something that does not use poll pressure. If you want her to learn to accept the contact doing it in a loose ring will help her understand. Right now she's nice a forward and you want to keep that. The loose ring is great for horses that have a tendency to lock up in the jaw and the poll.
What are your plans for her? She's a cute little stinker :)
A good rider rides transition to transition, a great rider rides half-halt to half-halt!