Using molecular dynamics and Monte Carlo simulations as well as analytical considerations, we study the arm-retraction dynamics of a three-arm star polymer in a narrow nanotube as a function of arm length, N, and tube diameter, D. The system dynamics is analyzed and compared to the bistable collective behavior of a pair of polymer chains tethered in a nanopore. The bistability arises from alternate flipping of one arm of the star into the pore section occupied to that moment by a single arm only. We derive analytical expressions for the free-energy landscape of an arm flip and determine the barrier height as a function of N and D. In the related case of two chains in a narrow tube, we demonstrate that correlations lead to a bimodal distribution of the chain-end positions whereas in a polymer brush, made of equivalent chains at the same grafting density, one observes a single peak only. The residence time distribution between consecutive arm flips is shown to follow a power-exponential relationship, demonstrating good agreement between theory and simulation.