Pencil,
Couple of things:
First, right brain/left brain is mostly a myth. Yes, the right brain has specializations, as does the left brain, but both work very closely together to accomplish very similar things.
Second, each eye is responsible for part of the information for each side of the brain. For example, on your left eye, the farther left portion, combined with the farther left portion of your right eye will send messages to your right side of the brain. The far right side of your right eye and the farther right of your left eye will send messages to the left side of the brain.
Laterlization of function isn't as divided as people might think. Split brain patients (those whom have their corpus collasums--the part of the brain that unites the two hemisphere--cut) are still able to process things very similarly to the way we do. Neuroplasticity plays a huge role in this case. Our brains are plastic, and will change functions if we need them to do so.
Secondly, if you're interested in attachment, you really should look at John Bowlby, Mary Ainsworth, Phillip Shaver, Peter Fonagy, and Daniel J Siegel (absolutely amazing--The Developing Mind is incredible). They are some of the most widely-known, highly regarded researchers in the field. Siegel's book "The Developing Mind" has a chapter on attachment, and it is one of the most easily understood, concise, clear explanations of attachment I have come across in my studies and research.
From the first time I heard about attachment in one of my psychology classes, I was fascinated. It truly does explain so much. My Psych prof explained it as: Secure "I'm ok; you're ok," Avoidant: "I'm ok; you're not ok," Ambivalent/resistant: "I'm not ok; you're ok," and disorganized: "I'm not ok; you're not ok" (and true disorganized attachment style are the serial killers--much rarer than you might think). You may have combinations of each style, but there will be a predominant attachment style, but even there it might be different for genders and ages. For example, I'm 100% ambivalent/resistant when it comes to males in the age of 40-55, but I'm secure when it comes to women of all ages.
We also have an internal working model, by which we understand relationships and how we attach to others. That informs our attachment behavior system, in which we engage in behaviors that are meant to accomplish the attachment we desire--such as proximity seeking, and so on.