There could be a lot of different things, some unrelated to dance, even, going on here.
First, though my kid doesn't do competitive team dance, she does do extensive ballet and modern dance (age 11), and classes of one hour and fifteen minutes are normal at this age and stage. So the length of this particular class is not unusual.
Second, you already know part of the problem: She's intimidated by the teacher. I know that the director sat in on this class and said it's not an issue in her eyes, but what matters is whether there are issues in your child's eyes -- the director of course expects a rigorous class and the director also is the person who hired this teacher, so naturally the director feels the class is fine. And probably it is. But if your child is not clicking with this instructor, or worse, frightened of her -- and stomach cramps and tears sure sound like fear to me -- there IS an issue even if it's not there for other kids.
Your child will encounter some tough teachers if she is going to continue in dance, and we all have to learn to cope with teachers who seem to be hard on us in particular. Has your daughter tried doing stretches daily at home? If so, did that help? If not, can you and she commit to her doing that -- you really do need to help out here and ensure that she is doing it, maybe at the same time every day. Make the environment for it pleasant; let her pick music or even do it in front of the TV if she can do that and still do the moves properly; whatever keeps her going a little longer. Reward her! A week of stretching X minutes every day gets her reward Y. There is NO harm in an additional reward here; saying "It's all for class" sounds noble but she is having a tough time and another small incentive is not going to spoil her. But you need to know -- it may not be a magic bullet even if she does stretch daily. She will get discouraged if she does it and the teacher is still on her case. But she could certainly try, and you can support her with a lot of positive talk and reinforcement.
She also: May be having growing pains or other real, physical issues. Is she developing breasts? Do the stretches have them down on their chests much, in which case frankly it would hurt her? You say she's not the most flexible -- one can improve flexibility to an extent, but I have read many times that there is certain point beyond which one cannot change the flexibility one got naturally; is the teacher wanting them to twist into pretzels?
She may be stressed by the dance scene outside this one class. Is she OK with her other classes, rehearsals and competitions? Does she enjoy them and want to go? Or is she a bit resistant, or maybe just quiet, when those things come up? It's possible that this class's toughness is bringing out a larger issue of her being stressed with the school overall, and/or the competitiveness and pressure of dance team. Does she ever mention, even casually, that other girls seem more talented, are more flexible, get better "parts" in the dance, etc.? She may be feeling she's not doing well but has to keep slogging on.
I would try to talk with her, at a time when she is calm and absolutely NOT when she is coming off any dance classes, rehearsals or competitions, and find out how she really feels about the whole scene -- the competitive nature of it, the other kids, the studio as a whole. Tell her up front that you are not going to judge her and she is free to express her feelings good or bad and it will not end up in her being told to do...anything. She may need to vent and if she thinks that will end with her being told, "Well you MUST keep on" or even "Well you HAVE to stop," she will hold back. Don't let her just shrug and say "It's OK except that one class." Find out what she does like about it, which teachers she likes and why, why she finds it appealing. If she can't come up with enthusiastic answers -- she may be drifting away from this activity and continuing it because "It's what I've always done" and she doesn't know, at 10, how to tell you she wants out and doesn't know how to define herself any other way. Kids at this age sometimes really feel locked into their one big extracurricular activity; they feel it IS who they are and they don't know how to cope if they want to leave it because then...who are they? If you feel that could be behind this, you and she need to have some very open communication and you may need to be open to her dropping dance.
If she is fine with everything except this one class, she may need to complete it but needs strategies just to get through -- Stretching at home; being ready to deal if that stretching does not improve; learning to take on board what the teacher says that helps her improve but ignore what seems like the teacher picking on her too much. Is there an alternative to this class? Another version of it at a different time with another teacher? You can say you have a schedule issue and just move her. But I know that often is not possible.
Someone else posted that you could shop for another studio. Good idea. Unless she is very close to other kids at her studio, you could look for one that is more supportive and possibly even for an outlet where she does non-competitive dance, if the competitive part is stressing her.
I would also talk with other parents of dancers her age and in her group. Do they too feel that this teacher is too tough? Do their kids also fear this class or feel they're being singled out? That gives you a read, sometimes, on the larger picture, though each kid is different.
Dance should be fun, not stressful, and rewarding, not dreaded. I don't believe in quitting but I also think you need to delve into this much more with your child, other parents and possibly the teacher again if this persists, especially after your child makes an effort to stretch at home.