The dynamical dissociation quenching (DDQ) effect is a new mechanism for laser-induced vibrational trapping of molecules in the infrared (IR) spectral range. Previously demonstrated for one-dimensional, prealigned diatomic molecules [see F. Chateauneuf, T. Nguyen-Dang, N. Ouellet, and O. Atabek, J. Chem. Phys. 108, 3974 (1998)], the effect was shown to result from a proper synchronization of the molecular motions with the oscillations of the laser electric field. The present paper explores the influence of rotations and misalignment of the molecular system on the DDQ effect. To this end, the two-dimensional (radial and angular) wave-packet dynamics of the H-2(+) and HD+ molecular ions are considered in an intense IR laser field starting from two types of initial angular distributions: The first type of distributions is appropriate for a field-free, pure angular momentum eigenstate and denotes typically an initially nonaligned, nonoriented molecule. The second type denotes a more or less well aligned and/or oriented initial condition, and is described by an angular width Delta which is considered a parameter in terms of which the efficiency of the DDQ effect are monitored. We demonstrate that the DDQ effect remains efficient whenever a proper compromise is achieved between angular localization and angular-momentum (action) minimization. From the detailed analysis of the time-resolved dynamics, a time scale is also estimated for the molecule-field synchronization process which underlies the DDQ effect. An ultrafast laser-induced rotational-electronic energy transfer is found to compete with the DDQ effect, in the case the initial rotational state denotes an almost perfect alignment and/or orientation situation. (C) 2001 American Institute of Physics.