My daughter's partner didn't stop when my daughter said "stretch".
OK, so the word that means "please stop stretching me" is "stretch?" Isn't that confusing? Maybe the other little girl who is new to the gym was confused?
In this situation, your daughter was voicing her right to be listened to regarding her body and what she was comfortable with. To me that is perfectly legitimate on your daughter's part and I do not get why the coach was "upset." Perhaps the coach should have had them switch partners to see if the issue was this particular paring or something else.
It sounds like you think some of the coaches like your daughter but others do not. I would suggest it is possibly not that personal.
Maybe it would help to look at this situation from the coaching "group management" point of view. I presume this is a practice with several little girls in it, all of whom are young and probably as a group not all that great when it comes to the skills of understanding/communicating/listening, all needing and deserving the same amount of attention and focus from the coach. At the same time the coach needs to keep the gymnasts and the practice tightly organized and moving systematically, quickly and safely from one event to the next. If there is more than one practice group happening at a time, as would be typical, they may only have the beam for X time and the bars for Z time. It's a lot to manage all at once and distractions make it harder. Even if there is no sass, one child asking lots of questions, making special requests, and making jokes would be disruptive and unfairly take up the coach's time and the group's time. I think it is great your daughter wanted to help her teammate feel better, and I am sure that joke was a big hit with the other girls. But maybe coming on top of everything else, that joke was seen by the coach as more disruption rather than appreciated as an act of generosity.
When it comes to asking for more reps, here are my thoughts because I have seen this before. One child doing more reps (and taking longer to complete their turn) than the others means the other kids get less time (unless there is enough equipment that no one has to take turns.) When learning a skill or doing reps as part of a group class, it is not about how many reps one
can do or would like to do, it is about how many reps the coach needs everyone to do so that everyone can have a chance to work what needs to be worked to the extent required in the overall time allowed. Perhaps your dd just needs this explained to her in a way that makes sense to her.
Obviously if a kid does not understand what is being asked of them, or needs to use the restroom, etc. they need to ask. But maybe she will get more responsive results to her questions when she learns to cut down on the unnecessary ones. I would suggest helping your daughter understand the difference between unnecessary and necessary comments/questions. Obviously this will be a process.