The only time one of my horses got sweated in a trailer was when my husband drove (that was the one and only time!) the truck and trailer...he wound up taking off way too fast, slamming on the brakes, etc...just as if there weren't a trailer with a horse in it on the back...we got to the place we had planned on gasing up and I checked on the horse, and he was wringing wet...needless to say I drove the rest of the way home (2 hours). I KNEW it was a direct result of how the rig was being driven as the horse had NEVER sweated up before, even on his first few trailer rides.
As far as your mare, I would definitely do short trailer rides until she is relaxed...and start out without even going anywhere. Load her, close the door, and unload. Etc... I would say even incorporate methods that encourage her to WANT to be in the trailer. Ie, work her around the trailer, and ask her to load, then take her back out, and do some more work. When she is comfortable self loading, and standing there calmly, then start tying, closing door, etc... It WILL take time, but I think this is something you can eventually get her over...be patient, and consistent with what you are asking, and how much you ask of her each time.