In this work, the entanglement dynamics of different subsystems such as atom-atom, atom-field and field-field with radiation field in squeezed coherent thermal states for the intensity-dependent double Jaynes-Cummings model (IDDJCM) and double Jaynes-Cummings model (DJCM) are investigated. The effects of both squeezed photons and thermal photons on entanglement dynamics is observed. The main feature of the double Jaynes-Cummings model - entanglement sudden death is observed for every subsystem. The effects of various interactions such as Ising interaction, single photon exchange interaction and dipole-dipole interaction on entanglement dynamics are studied. The effects of detuning, Kerr-nonlinearity on the entanglement dynamics are investigated for every subsystem. It is noticed that proper choice of the interactions parameters, detuning and Kerr-nonlinearity effectively removes entanglement deaths from the dynamics.