This study is the first to explore the interplay between haptic interaction and avatar representation in Shared Virtual Environments (SVEs). Specifically, how these factors shape users' sense of social presence during dyadic collaborations, while assessing potential effects on task performance. In a series of experiments, participants performed the collaborative task with haptic interaction under four avatar representation conditions: avatars of both participant and partner were displayed, only the participant's avatar was displayed, only the partner's avatar was displayed, and no avatars were displayed. The study finds that avatar representation, especially of the partner, significantly enhances the perception of social presence, which haptic interaction alone does not fully achieve. However, neither the presence nor the type of avatar representation impacts the task performance or participants' force effort of the task, suggesting that haptic interaction provides sufficient interaction cues for the execution of the task. These results underscore the significance of integrating both visual and haptic modalities to optimize remote collaboration experiences in virtual environments, ensuring effective communication and a strong sense of social presence.