The endoplasmic reticulum (ER) in plant cells forms a highly dynamic network of complex geometry. ER network morphology and dynamics are influenced by a number of biophysical processes, including filament/tubule tension, viscous forces, Brownian diffusion, and interactions with many other organelles and cytoskeletal elements. Previous studies have indicated that ER networks can be thought of as constrained minimal-length networks acted on by a variety of forces that perturb and/or remodel the network. Here, we study two specific biophysical processes involved in remodeling. One is the dynamic relaxation process involving a combination of tubule tension and viscous forces. The other is the rapid creation of cross-connection tubules by direct or indirect interactions with cytoskeletal elements. These processes are able to remodel the ER network: the first reduces network length and complexity whereas the second increases both. Using live cell imaging of ER network dynamics in tobacco leaf epidermal cells, we examine these processes on ER network dynamics. Away from regions of cytoplasmic streaming, we suggest that the dynamic network structure is a balance between the two processes, and we build an integrative model of the two processes for network remodeling. This model produces quantitatively similar ER networks to those observed in experiments. We use the model to explore the effect of parameter variation on statistical properties of the ER network.