  We study double ionization (DI) dynamics of vibrating HeH$^+$ versus its
isotopic variant HeT$^+$ in strong laser fields numerically. Our simulations
show that for both cases, these two electrons in DI prefer to release together
along the H(T) side. At the same time, however, the single ionization (SI) is
preferred when the first electron escapes along the He side. This potential
mechanism is attributed to the interplay of the rescattering of the first
electron and the Coulomb induced large ionization time lag. On the other hand,
the nuclear motion increases the contributions of these two electrons releasing
together along the He side. This effect differentiates DI of HeH$^+$ from
HeT$^+$.
