Aside from the whole injection question, perhaps you need to question whether this stable’s priorities are going to work for you long term. Having a new, young student get all the clothing and put on makeup to show in leadline may mean a lot of push to go to shows. IMO, this is common in saddleseat barns. Rider are less likely to trail ride or ride for pleasure, especially as they go up the levels. Saddleseat “brilliance” is more often achieved with short, intense workouts.
There are intense show barns in all disciplines at which the focus is on showing and time and money are focused on that. However, I think you are more likely to find a low-key fun lesson program that focuses on all-around horsemanship, fun, and partnering with your horse at a relaxed hunt seat stable. IME the value of 4-H and Pony Club groups is quite variable and depends greatly on the leadership. Though you will often find good groups associated with one of those “backyard” lesson barns.
I would suggest certainly taking the remainder of lessons that are paid for. At the same time, you can look around at other stables. As you finish with this package, you can look at places you can find through ads at your tack store and also asking people there. See if you can visit some barns (now that you have watched some lessons and seen the barn you have been using) and even watch a lesson.
Your daughter might well be sad about leaving this barn and you have to weigh that against the value of the program. One parent I know allowed the package to run out at one stable (kid knew how many lessons had been promised) and then waited a short time to see if daughter still wanted more. She then took her to a new stable for lessons.
Especially if your daughter is not a daredevil, you don’t want her pushed too far (a little is good!) so choosing the appropriate program is important. We hate to lose young riders!