On trying to discover a child strengths and weaknesses

I’m always upset with myself for not spending way more time with my children, especially with my older daughter, who’s turning five soon. But the day has only twenty four hours and I work and I also have a toddler, her brother, running around and getting into trouble all the time.
So I set up a special time daily when it’s just her and I, and I feel that everyday she’s grown already since the day before. This time is usually around bed time, when we can spend some quiet time together. We talk about anything imaginable, I read to her, and we sometimes share small stories about events that happened that day at my work or her preschool.
It’s a fun and wonderful time for both of us, and I think Adelina is now looking forward to this special time with me.
But I am not only looking for ways to enjoy ourselves during these hours spent together, I also try to get a better understanding of her strengths and also potential weaknesses.
Sometimes I think I can find myself in her, sometimes I believe I can see my husband there, but most of the time it’s just an exciting and new adventure that starts to mold my view of her.
She’s just so multifaceted and unexpected, that I cannot always know for sure what she will do or say next. And although she’s extremely absorbent for anything new, there are times when she just shuts herself off, so much so that she’s missing information she might otherwise acquire easily.
So I also started to better observe her during playtime and learn where her interests rest.
I also let her draw, write and paint as much as possible and she's always able to deliver a strong message thru these media. She seems to be thriving when given a way to express herself. But she seems sometimes shy when directly communicating with others.
These are just a few observations regarding my child. I have a lot more, but I just wanted to talk a little about the complexity of our children and how can a parent get an understanding of their child's actions, words and feelings, how and when to help, encourage or maybe restrict certain behaviors.
By trying to learn what types of skills and weaknesses my daughter possesses, I came across Howard Gardner's theory, stating and classifying different types of intelligence, as shown below:

1. Spatial intelligence - an ability to visualize the space with the mind's eye
2. Linguistic intelligence - a sensitivity towards symbolic language, the shades of meaning and the context, order, and resonance of words.
3. Logical-mathematical intelligence - an ability in maths and reasoning capabilities
4. Bodily-kinesthetic intelligence - the control of one's bodily motions and the capacity to handle objects skillfully.
5. Musical intelligence – the sensitivity to sounds, rhythms, tones, and music.
6. Interpersonal intelligence - an ability to feel and understand other's moods, feelings, temperaments and motivations.
7. Intrapersonal intelligence - an understanding of the self.
8. Naturalist intelligence - the ability to nurture and relate information to one's natural surroundings.
9. Existential intelligence - the ability to contemplate phenomena or questions beyond sensory data, such as the infinite and infinitesimal.

Now, after observing your children at play, after having conversations and maybe understanding them a little, just shoving their strengths into one of these categories is not possible, as it is more than certain that each child will have a combination of them, or even will have different degrees of skillfulness in each of these areas.
Encouraging them to further develop their greatest strengths is a no-brainer, but what about the areas you feel they don't master as much? Would you just forget about them or would you push them as well, for a rounded individual? Would this last approach hurt?

sources: http://en.wikipedia.org/wiki/Theory_of_multiple_intelligences