The Rosetta spacecraft is en route to comet 67P/Churyumov-Gerasimenko for a rendezvous, landing, and extensive orbital phase beginning in 2014. With a limited amount of available observational data, planning of the mission as well as the interpretation of measurements obtained by instruments on board the spacecraft requires modeling of the dusty/gas environment of the comet. During the mission, the collision regime in the inner coma will change starting from transitional to fully collisionless. As a result, a physically correct model has to be valid at conditions that are far from equilibrium and account for the kinetic nature of the processes occurring in the coma. A study of the multi-species coma of comet 67P/Churyumov-Gerasimenko is presented in our previous paper, where we describe our kinetic model and discuss the results of its application to cases that correspond to the different stages during the mission. In this work, we focus on numerical modeling of the dust phase in the coma of comet 67P/Churyumov-Gerasimenko and its interaction with the surrounding gas. The basic phenomena that govern the dynamics and energy balance of the dust grains are outlined. The effect of solar radiation pressure and the nucleus gravity in limiting the maximum liftable mass of the grains is discussed. The distribution of the terminal velocity of the dust grains as a function of subsolar angle is derived in the paper. We have found that in the regions with high gradients of the gas density, spike-like features can form in the dust flow. The obtained results represent the state of the coma in the vicinity of the nucleus for a series of stages throughout the Rosetta mission. The implications of the model results for future measurements by the GIADA instrument are discussed.