Karen, sorry, I don’t agree with your idea at all.
Emotional intelligence is exactly what it says on the label: intelligence about emotions. In other words, the ability to make conscious decisions about your emotional state, not only recognise it, but also influence it. And not only your own but also that of other people.
Why we don’t say “math intelligence” or “physics intelligence” is because, by definition, these are conscious areas of activity. I.e. they are parts of intelligence. I will not be surprised if “body intelligence” appears sometime soon. As a skill of being aware of your body and consciously controlling it.
Moreover, “intelligence” is what helps you to deal with unexpected situations, the ones you have not experienced before.
Let’s review your example: your daughter cries and screams when her blood is taken. The main question is whether this is a conscious, thought through rational action or not.
If it is, this means that she consciously recognises that she is feeling fear and, based on her knowledge about adults & doctors, considers screaming and crying the best action she can undertake to achieve a desired outcome. By the way, what is the desired outcome? A long term one?
A pretty devious scheme, isn’t it? :) The key here is that she acted proactively, and successfully achieved the desired outcome, right?
If this was not a conscious action, but a reactive behaviour powered by her fear — than it is as you say, a sign of lacking emotional intelligence. It doesn’t mean that she has none of it, it just means that current situation exceeds her combined capacity and skill for controlling her own emotions, as she desires. And this also reduces possibility of achieving her goal.
I should clarify here that there is nothing wrong with experiencing whatever emotions you have. They are just one of the mechanisms employed by your body. The problem arises when your behaviour gets affected by them more severely than it is necessary for a productive outcome. And there is also a question of social acceptance of these reactions.
EQ-enabled reaction will also allow you to change your emotional response if this is beneficial in the long term.
“If I want to help my daughter, I load her with ways to understand and manage the event before the event, not how to make herself more emotionally intelligent before the event”
Essentially, you say that you want to leave your daughter unprepared for unexpected and unpredictable events, because intelligence serves exactly this purpose. And to me this equals to intentionally harming her chances to live satisfying and full life in an unpredictableble reality.
Sorry, this is something I’m fighting against. I’ve seen too many people whose lives suffered from their lack of skill in dealing with their emotions.
Also, there is another “intelligence” we are all lacking in — “body intelligence”. Unfortunately, most people (myself included) haven’t been taught in a systematic way how we can better experience and control our body.