As many have said, it's not the discipline that should be the biggest decision, it's the trainer! And of course, one man's "good trainer" is another man's "bad trainer."
newhorsemom, as you mentioned, I think it is a great idea to go observe your local trainers in their lessons. Nail down what you'd like your daughter to gain in her lessons (equitation instruction, horse care, experience with a variety of breeds/temperments, just fun, horse-people interaction, etc) and figure out how she best can gain those things! Take notes if you have a lot of trainers to choose from. Take your daughter with you (I'm sure she'd love to go!) and see her reactions to the things the rider does in the lesson. Is she bored by what they're doing after 15 minutes? Is she grinning ear-to-ear? Is she begging you to let her ride there?
I know, when I take lessons, I want to learn proper show-type equitation, be very active with lots of variety, and have a strong trainer who makes decisions quick and motivates me (yeah, I'm cool with yelling to get my heels down!) On the other hand, it sounds like your daughter may want more of the fun horse stuff like learning to clip his ears and doing little patterns undersaddle (including learning safety and proper horsemanship) but without the MIL effect!
Anebel, as I was reading your (rant) post about english trainers and beginning riders, I was thinking to myself, "what is she talking about? I never experienced anything like that!" Until...I got to the part about putting the rider on a green broke TB! ha!! Yep, I remember those days! I was always a very confident rider, so I just thought it was fun! But I can imagine if a rider was unsure of their seat and was plopped on a 16hh TB 30 days off the track like I had been! I was always the guinea pig rider at one of the big lesson barns I rode at...any new lesson horse, I was the first one up! What fun for me!!