It's pretty common for kids to lack (to some degree) resilience/distress tolerance, but fortunately this is something that can be taught.
It starts with kids understanding what their emotions are-- being able to notice and name "I am frustrated" vs "I am sad" vs "I am embarrassed". Overtime they can delve into more nuanced emotions, to say "I'm excited" and know how it's different from nervous, worried, or scared. Knowing and naming lots of emotional states beyond just happy and sad is a skill that will improve their emotional health and ability to relate to others for a lifetime.
Some simple ways to start learning this are by reading children's books about emotions, making a simple chart with a bunch of feeling words and faces so your children can mark how they feel visually (for example by pointing, or place the chart on the fridge and let them put a magnet on the face that shows their current mood), and asking questions (or making guesses) about their feelings throughout the day. "Are you relieved the homework is done?", "Are you anxious about your first airplane trip, or are you excited? A little of both?"
You can also model emotional regulation by explaining your feelings, and healthy strategies of coping, out loud to them. "I really wanted to go for my run but it's raining! I'm so disappointed! I guess I should take a few deep breaths and then I can think of something else to do... Hm, ok, maybe I can do a yoga video instead."
Once she knows what her feelings are, and that she can use her words to identify them, introduce some "coping tools" to help her tame her emotions. There are lots of possible coping strategies, but some examples include: taking deep breaths, jumping rope or jumping on a mini trampoline, listening to music, counting to 10, splashing water on her face to 'cool down', squeezing a stress ball, cuddling a soft toy, or writing or drawing about her feelings. It might help to have one tool that's always available to use 'on the fly' for minor upsets (like deep breaths) and something more involved to provide daily emotional comfort (like listening to music and painting).
It seems that you have already noticed how much more effective validation and emotional support is, compared to reprimand, when she does have a meltdown. In the big picture, part of the goal is to teach her to seek emotional support in a healthy way, and to essentially provide herself emotional support when the situation/upset is small enough for her to handle on her own. When she is in tears, use supportive phrases like:
- I am here for you
- It is going to be ok
- This will pass.
- I can see you feel ___ because ____. (i.e I can see you feel frustrated because
your drawing doesn't look how you wanted.)
- Sad (angry/frustrated/hurt/etc) feelings don't last forever
- You can get through this.
- Let's hug/ Let's take deep breaths together/ Let's use a coping tool
Eventually, she should start to internalize the messages that it's okay to have emotions, it's not "the end of the world" when she experiences a negative feeling, and that her state of acute distress won't go on for too long. Understanding that the worst and strongest experience of our bad feelings is usually short-lived and 'this too shall pass' is an important aspect of emotional resilience even as adults.
As you daughter starts to understand that she can survive upsetting circumstances, you can gently introduce the question, "Is this a big problem or a little problem?" You can give her examples of "little problems" (drew a letter wrong, tried on an uncomfortable shirt, her juicebox is empty), medium problems (skinned knee, argument with a friend, lost a toy) and big problems (hurt or in danger, being bullied, something genuinely upsetting has happened). Have her practice identifying big and small problems, and some appropriate responses to each. For example, small problems can often be handled by letting it go, or taking a deep breath and trying again. Medium problems may need a coping skill and perhaps help coming up with a solution, big problems usually need an adult to help.
Expect it to take a while for the idea that some problems (that truly feel huge to her) are actually small to sink in, but over time she should begin to build the internal sense of a proportionate response to her situation. Encourage her and let her know how well she's doing if she begins to use coping skills or identify reasonable responses to problems on her own. Resist the urge to scold or react in disappointment when she doesn't- remind her that she has the tools to handle this setback, that you will help her, and that her strong feelings are not forever and will pass.
For more information, you may want to investigate "zones of regulation", "Building distress tolerance" and "building emotional resilience", which are all related ideas but come at it from slightly different angles and schools of thought.
Here's some quick links on the subject, but you can find many more online.