Isn't there a law that prohibits US citizens from traveling abroad to have sex with children who are legal in their country but are of an age that would be illegal in the US?

Is there really a "movement" on to prohibit interstate travel in quest for abortion service? Or is it merely rhetoric emanating from people who claim to be absolutely against abortion on demand?

I refer to the the radical "christian mob" - (note lower case "C" in the word christian is intentional). I have no doubt that cultish christian groups - the family of Fred Phelps for example being a prime example, would lobby for such restrictions - absurd tho they be.

If someone with great Political power and position, in any given State, wanted to try stopping interstate travel in search for an abortion it would be impossible to enforce it.

The idea itself is an absurdity to the point of making the very matter moot.

History tells us that all attempts to regulate morality end in complete failure. I offer two examples that support that fact:

The first example is "prohibition" of alcohol in early 20th century.

The second example is the illicit drug trade.

In both cases the "laws" prohibiting those things gave rise to highly violent and profitable underground / Black Market commerce.
It effectively came with profoundly negative unintended consequences.
One example would be that it generated a case load of such grand proportion that it clogged the institutions of Law Enforcement, and the court docket itself that it nearly paralyzed the entire system of justice in major cities across the country.
Another closely related consequence is the inhumane over crowded conditions in County, State and Federal Prison facilities.

Almost certainly prohibition against abortion likewise would create negative "unintended" consequences. There will undoubtedly appear an underground criminal enterprise. An illicit network of Abortion providers in literally every State where Abortion is outright illegal or at least severely restricted.

The old saw - "you can't legislate morality" will ring loud and true in the matter of prohibition on Abortion.
Gradually, over time, localities will cease to pursue enforcement and prosecution of violators who flog the Law - the prohibition on Abortion.

It will become tacitly "legal" in the absence of active enforced prohibition.

When that happens my only wish is that the financial burden for abortion services will NEVER be borne on the shoulders of the taxpayers - in any way, shape or form.
The financial burden must forever be privately funded.

I will put in thusly; Abortion services funding should NEVER be included with words like, Public Funds; Tax Monies; Government subsidies...etc.

Prohibition of abortion is one thing - Use of Public funds (tax money) is quite another.

I am arguing that "Prohibition" in practical terms should not apply to Abortion itself - because it really cannot be practically nor effectively enforced.
"Prohibition" should only apply to funding sources for Abortion Services regardless the determinate "necessity" for the Abortion requested.

The policy of prohibiting use of public monies removes the burden of moral culpability from the general public.
It necessarily places the moral responsibility solely upon the collective conscience of the people who seek to provide Abortion service as well as those who would have an Abortion themselves.