You have redefined the issue to support your contention.
Originally you put up the entire theory of evolution against the heliocentric nature of the solar system -- or so I interpreted your post, and perhaps I was mistaken in your intent -- and now you're talking about "animals changing over time" and the entire scope of planetary motion.
How does that occur? There are several good ideas, but that's a far from settled point.
Precisely, teach the theory, the good ideas, and make it clear what is solid and what is speculative.
Apples to apples, fact to fact, theory to theory. There is no more doubt about the FACT of a heliocentric solar system (the sun is measured to be approximately at the center of the solar system) than there is about the FACT of evolution (the flora and fauna preserved in one stratum look substantially different from the flora and fauna in other, well-separated strata). There are some open questions about the THEORY of the heliocentric solar system (the planets move in an approximately central potential that is dominantly generated by the sun's mass), just as there are open questions about the THEORY of evolution (species change over time through the mechanism of variation plus natural selection). The two are exactly parallel.
Precisely, teach the theory, the good ideas, and make it clear what is solid and what is speculative.
And do you actually believe that they teach "problems with the heliocentric theory" in public schools? If not, should the state legislatures step in?