Mobile robotic platforms that are expected to be engaged in applications domains characterized by unstructured terrains and environment settings will unavoidably face mobility constraints that may not be overcome by classical navigation planning and obstacle avoidance/negotiation tools. Endowing these robots with additional skills, which enable them to interact and manipulate obstacles blocking their pathway, will significantly enhance their ability to deal with such conditions, permitting them to perform their mission more robustly when encountering such unstructured and cluttered scenes. This paper proposes a novel hierarchical simulation-based push planner framework that searches for a sequence of pushing actions to move obstacles toward a planned goal position. This aims at overcoming obstacle challenges that block the navigation of the robot toward a target location and, therefore, can lead to the failure of the navigation plan and the overall mission of the robot. The planned pushing actions enable the robot to relocate objects in the scene avoiding obstacles and considering environmental constraints identified by an elevation or an occupancy map. The online simulations of the pushing actions are carried out by exploiting the Mujoco physics engine. The framework was validated in the Gazebo simulation environment and in real platforms such as the hybrid wheeled-legged robot CENTAURO and the mobile cobot RELAX.