Karl Cook actually did one of his Instagram “walking and talking” videos about this - it stems from tight/tense shoulders and back muscles. So if she can learn to relax her shoulders - (easier said than done if she’s braced for some hijinks) or perhaps warm up with stretches to be more aware of the existence of this tightness and how to relieve the tension, her elbows will then be closer to her side.
Sounds like you are making some good progress and getting to the root of things. If creeping her hands up the reins is part of it, go ahead and mark the “sweet spot” with colored tape, or even get the loops you can slide onto the reins. She probably doesn’t even notice she’s doing it, so it will help bring awareness, and hopefully comfort with the slightly longer rein.
To find more awareness in her body alignment (she probably feels like she is sitting up even when tipping forward) you can play the old game of going to extremes. Tell her to try being like a jockey, then sit down and lay back as far as she can. Then play with spots in the middle. You may snap some pictures to help her see where she really is. If you can come up with an imagery or catch phrase to go with her deep, tall seat, it’s something you can call on when she’s tipping (my female friend/trainer used “Sit Baaaaack!” with a man’s German accent on me and it’s stuck ever since! You could also try things like “Ride like the queen/for dressage gold/etc”).
And as others have said, physical tension anywhere in the body does no favours here… in that case a lot of the traditional exercises we do with beginners can actually make for a great warm-up routine. Arm circles, touching the ears and tailhead. Dropping stirrups to do some ankle circles and knee hikes. I also like simple shoulder circles and “shrugs” (where you squeeze the shoulders up to the ears, and then let go and drop them all the way down) because they are easy to do any time in a ride when tension creeps in.
This is just a shot in the dark, but would some “egg and spoon” or “carrying a mug full of water” exercises help?
You have some great ideas here, and I wanted to chime in to say that there is absolutely no harm in letting your daughter spend time on the lunge line until she truly is more comfortable on the horse, then slowly work towards being more independent off the lunge. While it will feel like you’re moving at a glacial pace to begin with, she will quickly progress once she feels safe and comfortable. Taking the time to make her feel safe now, especially since she’s had some bad experiences, will take far less time in the long run than trying to undo further bad experiences.