And if you think the law steps over the line for states to "run their own show", you might want to re-read the introduction that gives a very explicit explanation of why abortion regulation affects interstate commerce. Whether you personally agree with the reasoning or not, lesser justifications of interstate commerce have been taken to court (and won).

Also, when it comes to the rights of citizens, the Federal government has the ultimate authority to enforce those rights. Whether you agree with something being a right or not, once the Federal government -- whether Congress or the Supreme Court -- determines something is a right, it trumps any laws that the states may have. Roe v. Wade established that at least in the U.S, choosing your own state of pregnancy (or lack thereof) is considered a right. So this legislation would trump any state laws, just as Roe v. Wade (technically) is supposed to trump state law.