Physics does not have such an easy concept of "universes within universes".
In classical physics, (if we even allow the notion of varying the number of spatial dimensions) the number of dimensions of the universe dictates a lot of fundamental behaviour. The prime example is the behaviour of the electrostatic or gravitational forces, which scale as $\propto 1/r^2$ with the distance from their sources, essentially because the surface of a sphere goes with $\propto r^2$ in 3 spatial dimensions. Consequently, one expects that universes with $d$ spatial dimensions have force laws that scale as $\propto 1/r^{d-1}$.
But this means that you can't just "embed" one universe in another! A charge (or mass) cannot simultaneously exist in a universe where the force it exerts scales with $1/r$ and one where it scales with $1/r^2$, since then the 3d force does not properly restrict to the 2d force. So the concept of embedding universes, if such a thing exists, must be more subtle than one would naively assume.
In modern field theory there is however, both classically and quantumly, the notion of dimensional reduction or compactification. The simplest instance is Kaluza-Klein theory, where a four-dimensional universe with gravity and electromagnetism emerges from a five-dimensional universe with only gravity whose fifth dimension is compact, which in this case means it has the form of a (very small) circle instead of being infinitely extended like the dimensions in flat space $\mathbb{R}^3$.
In this scenario (which has many other variations on it such as brane cosmology with the Randall-Sundrum model as its archetypal example), the physics in the higher-dimensional universe (the bulk) and the lower-dimensional universe (the brane) are markedly different. The physics of one are not the naive restriction or extension of the other - they observe different fields, different forces, essentially entirely different laws of physics. It is crucial to note that the physics of the brane are entirely derived from the physics in the bulk - there is nothing that is "solely on the brane".
In this context, it is not clear how one would interpret your question, since there are no genuine "lower-dimensional objects" here - everything that lives in the lower-dimensional universe is induced by objects in the higher-dimensional universe, and still follows the laws of physics in the bulk, however different they may appear if one just restricts to the brane. There is no interaction like "pushing on the circle only in 2d", since both the circle and the objects pushing on it are all essentially slices from the higher-dimensional manifold, and what manifests as "pushing in 2d" has a corresponding - but not necessarily recognizable - action that happens in the bulk.
