I think the problem lies in the fact that "space expands" is just a metaphor for the mathematical description of the expanding Universe, in which the proper distance between comoving points increases with cosmological time.
When you look at a gravitationally bound system, like a solar system, the planets have been sprung free of the Hubble flow because they are gravitationally bound to the sun: there is no viscous "space expanding force" trying to disrupt their orbits by shoving them away from the sun. So an appropriate GR metric for thinking about the solar system might be the Schwarzschild metric, which includes no terms that could be interpreted as "the expansion of space".

So applying the "expanding space" metaphor too seriously gets you into tommac's situation, in which you wonder if space is "really" expanding within the confines of the solar system (and being ignored by the planets) or if space is somehow nailed in place by the existence of gravitationally bound orbits. I believe this is a question with no answer, because it arises from a misapplied metaphor.
But of course I'm ready to be corrected by those with a better grasp of GR than mine.

Grant Hutchison