All motives that people have for anything can be tracked down to a single quest: The longing for love.
It can be the feeling of love in oneself, or being blessed with somebody else's love, or a couple of other kinds that exist.
On a psychological level your question is really complex and I truly believe neither can it be answered just like this nor can we diagnose what's going on based on just a few lines from you and without knowing anyone of you in person or observing the situation you're describing.
However, taking what I said in the beginning, two things are given:
(1) Your daughter is longing for love, (2) Your daughter is experiencing some kind of pain in the situation.
I do not want to give specific instructions here about what to do and what not to do on a behavioral level, because it makes no sense without really knowing what's going on there, but I'm very sure that it will help if you can feel both aspects (1) and (2) as clearly as possible in the very situation. What I mean is feeling them so clearly that it really moves your heart, each single one of them clearly moves your heart individually. This is not a one-time exercise (or maybe not even an exercise at all), this is something you may need to practise for a while in the type of situations you described.
Don't expect it to be easy, there's a high chance that you've also learned and cultivated to suppress, deny, or control your longing for love and some types of pain you've been carrying within. These things will be obstacles as you try to be truly sympathetic with your daughter, so it will also help if you work on your own issues at the same time.
If you really reach the point where you deeply feel her longing for love and her pain in the situation, you will somehow naturally help her transform the problem. I can't predict how exactly it will happen (nor could I describe it afterwards), but I guess you will feel such an intense love for her and you will express it to her (which will probably involve some kind of touch or look or hug or anything) in such a way that two things happen automatically:
1) The love you're expressing in that moment will not be just a momentary experience for her, it will rather be implanted as a lasting experience in her heart. With this there a lot of things will feel different to her, and I'm quite sure these situations won't happen the same way again. This effect involves no time, just intensity. Given the right intensity of love it can happen in an instant.
2) The pain she's experiencing will be released. Most people don't know how to deal with pain, so they ultimately just try to get rid of it through distractions or suppressing it (e.g. by willpower or by pills). They deny the fact that nothing is just gone because you refuse to look at it. The same applies to your daughter: Whatever pain she's experiencing, ultimately it must be confronted and felt to be released. This in turn can be difficult because it requires total submission to it.
Adults are usually unwilling to do it, at least in everyday life and as long as it can be avoided, but for kids it's somehow the natural state. They don't resist their pain. Their problem is that adults around them have a tendency to hinder them from feeling their pain freely because they see it as a sign that something is wrong and they want to stop it. This perspective is not wrong, but it confuses things a little. Yes, pain is painful and it's natural you want to be free from it, and there's nothing wrong with this, the kid wants it too, but feeling it IS solving it, distracting yourself from it IS NOT solving it. So if you want to help your child to release the pain that is there, just help her feel it totally.
Now, the difficulty here is that "totally" means nothing less than 100%. Even just 99% won't work. You must jump and let go of all resistance.
If you as her parent resist her pain in some way, I see a high chance she can't reach 100% either, at least not easily.
This is where love comes into play again. True love incorporates total acceptance. As your love for her deepens in the situations you're describing, you will be able to hold and support her as she's in pain with total acceptance, and in this setting she'll be able to feel totally what's there, thereby getting free from it.
In fact if you really hold her in total acceptance and love, you will feel her pain too, and as you feel it for her, you help her release it.
What I'm trying to explain may be a little abstract, and indeed it's nothing to really comprehend. It makes no sense on a psychological level, so don't even try to understand it in psychological terms. But I have an example which might make it a little easier to comprehend: Have you ever experienced that a love relationship had a transforming effect on you or your life? I'm not talking about ordinary things that happen in a relationship like learning something new or re-evaluating your life or moving to another city, I'm talking about a transformation that happens just because the love is so intense, and with no further effort from anybody's end. "Transformation" meaning that something is changed from its roots in a way you could never have done it with your normal means, and in a permanent way that lasts beyond the duration of the love relationship. Chances are you've experienced something like this before. This should make it easier to understand my main points here:
- My answer is NOT a psychological answer. Like said, I don't see a psychological answer possible based on the little details we know. It should not be read as a psychological answer either.
- My answer suggests things that you can do, but ultimately it's about not doing anything because you reach a state of total acceptance and love of what's there. This is very important to note.
I'm in no way implying that you don't love your daughter or have not loved her in the past or have done anything wrong in the past.
It's more like that the time in the womb, during delivery and the first years are very sensitive times in a person's life. It's hard to predict from outside how certain things that happen are experienced and interpreted by the baby/infant that does not have abstract thought or the ability and experience to reflect yet. Likewise it's certain that there are painful experiences, and the fact that you have twins makes me assume there was even more potential for them, for instance during the delivery. All of these things are really difficult to investigate into. This is nothing to be done here. But the good thing is that at least love and acceptance are forces that can fix these things without having to understand details a lot.
Furthermore, when I'm advocating in favor of feeling pain and avoiding distractions from it, I'm in no way implying that anybody should stop any treatments they're receiving or anything of that kind. In other words: When I say love and acceptance, I'm in no way trying to implement another kind of resistance and non-acceptance through the back-door.
To add some psychological thoughts too (not meant as an answer, more like some hints): It's common in toddlers to be less able to regulate frustration. Chances are high that this is a valid part of the explanation in your case. The age between 1.5 and 3 is usually the core period when the infant develops an own will, and it's a learning process to learn to handle it. Others have already pointed out approaches to help your daughter learn it more effectively.
Likewise it shouldn't come as a surprise if your other daughter develops similar behavior patterns too in a while.
At the same time I personally believe that most these situations have strong influences from the past too. Or in other words: It's hard or at least harder to thoroughly frustrate a person who isn't already carrying an unresolved frustration from the past. While it's always a good start to address present frustration in the present, in your case with paying attention to basic things like hunger, sleep, attention, touch, security, sharing emotions etc., it's always important to realize the importance of the past as well.
It should have become obvious that exploring the past, especially with a kid of that age, is beyond what we can do here.
I'm currently even unable to guess how these situations really are and how severe and disturbing and disrupting it is. If it's really severe from your personal point of view, seek professional advice in your area. If you're just confused, chances are high that it's totally okay to watch, nothing serious is going on, and in a year or two you'll see a much clearer picture.
Trust your intuition and your instincts. Don't be too worried just because your daughter is experiencing strong emotions. It's normal. Don't be worried either that your kids are different. They're unique, and they will always be.