I like the idea of letting you dd "have" her own gymnastics experience, but don't fall in line with the idea that you need to "keep your mouth shut" to accomplish that. Your stress from the first meet isn't that your dd did poorly, but rather that her meet didn't go well for her. There's nothing wrong with feeling bad about her meet as long as you're feeling bad about how she had to absorb the feelings she had after bars and beam. There's a lot of drama that goes into a "first meet", and a couple of falls can really send a kid reeling, so you had, and did, tread lightly.....good job.
The problem you need to help her with is her form. Her coaches can only do so much with reminders, but it's up to her to embrace the notions that she's capable of good form, can raise her scores by making it a priority, but most of all.....can have so much more success and consistency with her skills by doing them with good form.
Most kids, parents, and even some coaches see good form as an entity, in and of itself, that raises scores by eliminating deductions for bent knees, flexed toes, arched backs, and the bent elbows caused by arching. What's missing is an appreciation for the simplicity of movement that good form brings to the gymnasts efforts.
It works like this.......
The kids learn skills through a process that usually ends in lots of repetition to refine the skill and to build consistency through muscle memory. Most of us only have a certain capacity to remember things, as there's a limit to how much we can ask of our selves, and the same is true of our muscles. The challenge imposed by poor form is that a variable is introduced by every deviation from straight legs, pointed toes, tight core positions, correct head positions, and straight arms. That means that poor form requires a kid to learn how to move through a clear hip that accomodates a different distribution and placement of body mass, and that child will have to learn many variations of the skill.....one for slightly bent legs, one for severely bent legs, another for bent legs with an arched back, with bent arms, with legs flopping around, head sticking out...........It can get to the point where a child can only attempt the skill and hope for the best because they simply don't have the mental and/or physical capacity to learn fifteen different versions of a clear hip.
The only way out of this dilemma is for the kids to buy into the concept that form, while adding to their task, will simplify the task in a significant way and make it so much easier to learn and have fun with skills that suddenly become easy to do. It's really that simple. Good form and body positions allow the kids to concentrate their learning on skills that offer the same challenge each time, rather than the fifteen variable challenges created by form and position deviations.
I don't know how you can frame the concept for your dd, but here's how one mommy did it. She constanly put things her dd used in different places, making even the simple task of getting a cup for water a burden, and she changed it every day for several days. Her dd got upset with her mother after 3-4 days and told her to stop changing things around so she could count on things being where they were supposed to be. Mom changed things back to the way they were and a couple of days later had a fun chat with her dd about what the whole experience was about, and related it to how consistency makes things easier....even if it took a couple of hours to put things back in order.
So while you should "keep your mouth shut" about her "bad meet", you could think about the form/consistency/burden conundrum, and find a way to help your dd come to the reality that she's spending a whole lot of gymnastics bucks and not getting what she wants for "her money".