Is it that space is not expanding within the smaller structures or is space expanding through these structures?
where I've highlighted what I think is the key issue.
The phrase space is expanding is a convenient metaphor to describe the expansion of the universe, but it is only a metaphor and taking it too literally can lead to confusion. It this case it's leading you to ask if space is somehow sliding past gravitationally bound masses. Or to use the rubber sheet analogy: if we model the expansion of the universe by an expanding rubber sheet, does that mean gravitationally bound masses are sliding over the sheet so they can stay together while the sheet expands?
The expansion of spacetime has a precise technical meaning that is derived from the FLRW metric that describes our universe on the large scale. If we use coordinates in which spacetime is isotropic and homogeneous then the proper distance between any two points in space is a function of time. Yes, we can describe this as space expanding, but this is an interpretation that is specificially linked to the FLRW metric.
The problem is that near a massive body spacetime is no longer described by the FLRW metric. If we consider a single massive body then very close to that body spacetime will be described by the Schwarzschild metric. This is time independant and there is no sense in which it describes an expanding, or contracting, or changing in any way spacetime. The concept simply isn't appropriate. Far enough away from that body that its gravity becomes negligable we're back into a region of spacetime described by the FLRW metric, and we can use expanding spacetime as a reasonable interpretation of the geometry.
The point I am trying to make is that your question doesn't have an answer because it doesn't mean anything. And it doesn't mean anything because you've taken a concept (expansion of spacetime) that is specifically linked to the FLRW metric and tried to apply it when the FLRW metric doesn't apply.