First off, you did get the acceleration correct for the system. As for the small block being pushed by the large block, keep in mind that for the small block to accelerate at 2m/s^2, the mass you will need to use is that of the small block, because after all, you are concerned with the motion of the small block, and its mass, or resistance to external forces, is the issue at hand.
Another point is that pretend the question told a bit more, in that a person was pushing the crates with force 300N, instead of that being ambiguous. Analogously, person:2 blocks is comparable to large block:small block. When you were solving for the motion of the 2 block system, the mass used is that of the objects that are to be in motion, not the hypothetical person/object delivering the force. In fact, you do not even need to know anything about the source of the 300N applied force, because is does not matter for the movement of the 2 block system.
Again drawing on the comparison of person:2 blocks::large block:small block, to find the force necessary to push the small block at 2m/s^2, all you need to know to calculate and describe the force on the block are the acceleration and mass of the object in motion, not of the source of the force.
