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Reconnections and interactions of filamentary coherent structures play a fundamental role in the dynamics of fluids, redistributing energy and helicity among the length scales and inducing fine-scale turbulent mixing. Unlike ordinary fluids, where vorticity is a continuous field, in quantum fluids vorticity is concentrated into discrete (quantized) vortex lines turning vortex reconnections into isolated events, making it conceptually easier to study. Here, we report experimental and numerical observations of three-dimensional quantum vortex interactions in a cigar-shaped atomic Bose-Einstein condensate. In addition to standard reconnections, already numerically and experimentally observed in homogeneous systems away from boundaries, we show that double reconnections, rebounds, and ejections can also occur as a consequence of the nonhomogeneous, confined nature of the system.