Under nonlinear interactions with different forms of intensity-dependent coupling (IDC), mixed moving atom entanglement transferred from the two-mode SU(2) coherent states (SUCS) is investigated. It is found that the atomic motion related to the field-mode structure parameter (FMSP) can make the atom entanglement evolve periodically, but can also destroy it severely. When the FMSP increases, the atoms are completely disentangled, irrespective of time and the initial atomic state without IDC. But under suitable forms of IDC, the atom entanglement not only revives, but also gets great enhancement and keeps the periodicity of its evolvement, even for the initially mixed atomic states. The maximum atom entanglement can be derived for proper values of the parameters of the SUCS.