First of all, I only have one kid, who recently got out of the toddler years, so I think it’s so amazing that you’re sane enough to even collect your thoughts on all of this! The toddler years are so hard. Reading this, I related so much. I’m not an angry person, either, and hated showing that anger to my son. I would shock my friends and family sometimes, with how much I’d yell or how upset I’d get.
One piece of advice no one gave me is, if you can afford it, don’t feel guilty about putting your daughter into a daycare/preschool/kids activity of some kind. It will give you a break but also give her a different way to get out energy. Even if you just get a babysitter and go somewhere with your twins, or have the babysitter take your daughter to the park or something, anything that will give you a break can really help. When my son started going to daycare, and then preschool (we live in France where, thank God, these things are subsidized by the government), it changed my life. I have friends in the States who started their toddler in a sort of extracurriculat program every Monday afternoon and she’s also doing great. Do not feel guilty about doing something like this if you can. It will help you stay sane, which will make you a better parent, and it will benefit your daughter by making her more social, learn new things, etc.
Another thing to remember is, it’s hell right now, but it will get better. Remember that this is only temporary.
Another thing that helped me was distraction. So if my son started insisting he wanted something or had to do something or was generally being rough, and rational explanations or a firm “no” didn’t do the trick I would totally change the subject, like “Hey! Do you want to read a book together?” Or just simply take him out for a walk (in his stroller if I knew it wasn’t a “walking day” for him). Sometimes, it worked. I know this isn’t always easy to do with a toddler but it could be worth a try.
Also, the book “Toddlers Are A**holes: It’s Not Your Fault” by Bunmi Laditan made me laugh so hard whenever I’d read it, and really comforted me. I’d definitely recommend it!
Most of all, hang in there. Remember that it will get better and that in the meantime, especially as your daughter starts talking more and developing her own personality beyond the toddler-ness, you will have more and more pleasant or even downright amazing moments together. Sending a hug from one mom to another.