  We develop two novel models of the H$_2^+$ molecule and its isotopes from
which we assess quantum-mechanically and semi-classically whether the molecule
anti-aligns with the field in the first excited electronic state. The results
from both models allow us to predict anti-alignment dynamics even for the
HD$^+$ isotope, which possesses a permanent dipole moment. The molecule
dissociates at angles perpendicular to the field polarization in both the
excited and the ground electronic state, as the population is exchanged through
a conical intersection. The quantum mechanical dispersion of the initial state
is sufficient to cause full dissociation. We conclude that the stabilization of
these molecules in the excited state through bond-hardening under a strong
field is highly unlikely.
