Ab initio quantum chemistry is used to generate a three-dimensional reactive potential-energy surface for the collision of S-1 Al+ ions with (1)Sigma(g)(+) H-2 molecules. This surface, in a tessellated and locally interpolated form. is used to generate forces for classical trajectory simulations of the 3.98 eV endothermic Al+ + H-2 --> AlH+ + H reactions with initial conditions appropriate to a thermal H-2 Sample and an Al+ beam of specified center of mass collision kinetic energies in the 3-20 eV range. Our findings indicate that the reaction occurs not on (or near) the collinear path, which has no barrier above the reaction endothermicity, but via a near-C-2v insertive path which spontaneously breaks C-2v symmetry via second-order Jahn-Teller distortion to permit flux to evolve to AlH+ + H products. The strong propensity to "avoid" the collinear path and to follow a higher-energy route is caused, at long range, by the ion-quadrupole interaction between Al+ and H-2 and, at shorter range, by favorable overlap between the H-2 sigma(u) and Al+ 3p obitals. Examination of a large number of trajectories shows clearly that reactive collisions (1) lose much of their initial kinetic energy to the repulsive ion-molecule interfragment potential as the closed-shell Al+ and H-2 approach, (2) transfer significant energy to the H-H stretching coordinate, thus weakening the H-H bond, (3) convert initial H-2 rotational motion as well as Al+ to H-2 collisional angular momentum into rotational angular momentum of the HAlH+ complex, "locking" the H-2 moiety into the insertive near-C-2v geometry about which twisting motion occurs, and (4) allow the Al+ ion to form a new bond with whichever H atom is nearest it when the system crosses into regions of the energy surface where the H-Al-H asymmetric stretch mode becomes second-order Jahn-Teller unstable, thus allowing fragmentation into AlH+ + H. These findings, combined with considerations of kinematic factors that distinguish among H-2, D-2, and HD, allow us to explain certain unusual threshold and isotope effects seen in the experimental reaction cross-section data on these reactions.