Dynamic obstacle modeling in stage/gazebo

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Stage does not do physics-based modeling or simulation of a robot with multiple joints (e.g. by applying forces to those joints). Stage in general assumes a very simple model for the vehicle, simply integrating the linear and angular velocities with respect to the configured timestep to update the position. I don't think it can model collision after-effects at all.

You should look at the Gazebo simulator if you want a simulator that actually runs a physics engine to do the simulation (allowing you to e.g. specify a force on a joint and Gazebo will figure out, based on friction and inertial constants and such, how that force affects the robot). I'm not sure if Gazebo handles things like what happens if your robot impacts something and could cause it to slide off in a different direction, but it definitely has a better chance of supporting that than Stage.