Wow, I've never heard of a horse trying to balance like that.
Have you tried loading her and just leaving her in the trailer to eat her dinner, then taking her out? Does she just stand in there with no problem?
Is your trailer a straight load, or slant load?
How long have you had your mare? What type of trailer did she ride in before?
Is the trailer completely enclosed, or can you take the tops of the doors off like on some trailers? If you can, have you loaded her, then had someone watch from behind as you travel down the road to see what she's actually doing? I think that's where I'd start. Just down to the end of the driveway and back, or no more than 100 feet down the road. Try to determine at what point or speed this seem to be happening, then try to fix the problem from there.