Action and reaction
You omit to give a mechanism for construction other than a semi plausible "inflation". As young engineers we joked about "sky hooks" but as with all things formerly implausible, such as space elevators, these are now a reality see wiki. So tethers during construction would aid stability on completion and provide a temporary framework for supporting the outer shell. If the planetoid is mined for obtainium to use for the tethers and shell then the orbit will not change as the total mass is unchanged.
How many tethers are required? Mathematically four (tetrahedral) would be the absolute minimum, diametrically that becomes eight, say a safety factor of three in pairs for redundancy /maintenance then 12 pairs of obtainium to the core (similar to those shown in photo) and 30 obtainium (green) for the lattice should be enough for a blue inflated translucent unobtanium Icosasphere. Which tethered together rotate together Click to see animation by Illustr CC BY-SA 4.0 Note I have truncated top and bottom as more economic and less problematic to produce 2 level platforms
Concept of spherical objects with one suspended inside another**
If inflation during construction is uniform on opposite sides the system will stay self centric.
kingledion raised the issue of solar winds but earth is not pushed into outer space, any additional mass will pull the planetoid inwards etc. Equally if containing conductive strands the lattice frame acts more like a faraday cage (with it own electromagnetic issues, but a wide open lattice will not cause hardship).
kingledion, <PERSON> et al. 24
Have in general pointed out that there are similarities to <PERSON> shell theory and there would be nothing to stop the planet and shell moving at different rates thus on completion over time the core and case could drift into one another. Using diametrically opposite tethers will stop any such drift.
The "space anchors" would provide an interface for space elevator occupants to transfer to the 12 orbital spacepads, and the lattice could be used for monorail links between them. Given the layout any failure/maintenance would still provide a choice of back-up routes. However due to the spin the shell shape is likely to be squished top and bottom, so 2 polar spaceports would make more sense. To counteract the inward pull at the poles a pillar or stanchion form support is needed as proposed by rek ? these could be triangular in nature to align with the truncated oblate (flattened) spheroid.
What could create a calamitous wobble with a catastrophic collision is significantly uneven internal weather, or a drastic external collision event. Both of these would be mitigated by use of tethers.
In either case with enough force the "skin" could rupture or exceed the tethers strength and the whole system instantly collapse. But then unobtainium is indestructible, per your specification ! 302