If you haven't already, might I suggest you have a careful look at the concept of the "ethic of care" (e.g., Nel Noddings, among others; and also Shapiro & Stefkovic). In terms of how one might conceptualize emotions - huge area. If you have not come upon Megan Boler's book, "Feeling Power," it's a must-read. I will be posting a paper shortly on emotions and reasons - the relevant part of that might be a (brief) overview of the different disciplinary treatments of emotions (philosophy, psych, etc.) that I think might be helpful to settle on a conception for your work.
Based on experience and literature, I am of the opinion that emotion is part of care in teaching. Our students are from diverse background and therefore, experience various range of issues in their learning process. Many at times, we have rendered help emotionally and cared for them without neglecting their well being. Please check out the following link for more information.