I doubt you recall being 2yrs old vividly. Or even 3. Around this age feelings get really really big. There is no concept of emotional regulation yet. That's on the parents to teach. I don't know you, but you did say that solving problems feels good for you. Eventually, just working through problems would have taught you emotional regulation.
From my own experience with my toddler, validation doesn't always work. Sometimes feelings are just big, and we just need to be in them for a moment. That's also a nice lesson for them. It teaches them that big feelings come and go, which teaches them not to be afraid of big feelings.
I'm on a tangent now - the hardest part isn't necessarily helping them calm down. It's getting them to hear you and see you in the hard moments. If you can't get them to hear you (in a calm way) none of this works.