Crying for pain is fine.

Crying for emotional manipulation is not permitted.

The kids can turn off the tears when they want if the manipulation is shown as ineffective

When you put it this way, it seems more reasonable. Obviously you shouldn't reward or validate tantrums. At the same time, however, empathy is an easy way to acknowledge misplaced emotional reactions without encouraging them.

Meeting a tantrum with "I know you don't like the taste of vegetables, but they're an important part of growing up and you must eat them before having sweets." is different from "In this house, you cannot cry if there's no real pain."

There's no fine line between valid responses and manipulation. For manipulators, the pain FEELS real. The pain is a part of a learned behavior. Guiding those feelings instead of making a hard rule cutoff will have better results and build better trust.

This is the fine line all parents walk.

On the one hand, I agree that it is important for children to learn that manipulation is not the best way to get the things that they want. On the other hand, I think it is also important for them to learn that they can trust their parents to be there for them when they truly feel they have a problem, even if it isn't physical pain, and even if it is really quite silly. But you don't want them to learn that they can't trust you, because someday they might have problems that aren't silly.

Today it might be "the socks you picked out for me aren't the right color and the boys at school will make fun of them". But tomorrow it might be a developing drinking or drug problem or early signs that a romantic interest is becoming abusive. If they learn they can't bug you about the socks, they might also learn that they can't bug you about those things either.

They're toddlers so discussion about drugs, peer pressure, and other abuse is discussed.

Those are well managed. I practiced tonight with name calling.

After preparing him I insulted my oldest.

I said "you have donkey breath"

I asked if what I said was true. "No." Okay. Now you have power and I have none. Lies cannot hurt you. Insults are lies. No one can harm you with words if you know who you are.

And if you live with a toddler, even those have to exist and are necessary for becoming a healthy being. At least if they are met with understanding by the parents.