The "validate and problem-solve together" approach doesn't work reliably with adults. For people who are single-mindedly out to get what they want, it's not the first time someone has tried this on them, and they've learned the counter. When they realize that validating their emotions is a priority for you, they'll insist that your validation is insincere unless you give them what they want.

"It's easy to say you care about my feelings, but since you aren't [giving me what I asked for], I see what you're really about."

"If you really cared you'd...."

"If you really understood you'd...."

Toddlers haven't learned the next step of the game.

My MIL with dementia does this. I typically respond by saying, "you don't mean that" or "I did not do such a thing". If she keeps up her a mile a minute hostile diatribe, I start praying very LOUDLY. That appears to be the only thing which gets her to be quiet and calm down.

There's a counter for that as well but I can't quote the verbal self defense book right now. But one of the main defenses taught in the book I have is against "if you really" pattern.