my wife is considering writing (and selling) some childrens' books which will contain songs which are to the tune of various copyrighted songs (like the "Let It Go!" song from Disney's Frozen). She wouldn't have the musical notes in the books. My question is, would it be legally kosher to say that a song is "to the tune of Disney's 'Let It Go!' from Frozen"?
Such a song would probably be a derivative work, and thus permission would be required. If the rhyme scheme of the original was imitated, or other distinctive elements were used, the case for this being a derivative work would be even stronger. Of course, the copyright owner might not sue, but with Disney ...
It might be that permission could be obtained. There is no knowing until she asks.
She should probably consult a lawyer with knowledge in this area with the specific song(s) she plans to use.
Parody and Fair Use
Strictly speaking, this would not be a parody, because it is neither mocking nor commenting on the original. Rather it is using the form of the original to say something quite unrelated to the original. Many people mistakenly use "parody" for this situation. However, whether or not this is a "parody" it might be fair use if this is under US law. A finding of fiar use is not automatic for any parody under US law.
Note that in Suntrust Bank v. Houghton Mifflin Co 268 F.3d 1257 (The case of The Wind Done Gone (TWDG)) the 11th Circuit Appeals Court did not simply dismiss the infringement claim on the ground that this was a parody. Rather it undertook a detailed study of the factors governing fair use. The court wrote:
There is no bright line that separates the protectable expression from the nonprotectable idea in a work of fiction.
While we agree with Houghton Mifflin that the characters, settings, and plot taken from GWTW are vested with a new significance when viewed through the character of Cynara in TWDG, it does not change the fact that they are the very same copyrighted characters, settings, and plot.
Houghton Mifflin argues that TWDG is entitled to fair-use protection as a parody of GWTW. In Campbell, the Supreme Court held that parody, although not specifically listed in [17 USC] § 107, is a form of comment and criticism that may constitute a fair use of the copyrighted work being parodied. Parody, which is directed toward a particular literary or artistic work, is distinguishable from satire, which more broadly addresses the institutions and mores of a slice of society. Thus, " [p]arody needs to mimic an original to make its point, and so has some claim to use the creation of its victim's . . . imagination, whereas satire can stand on its own two feet and so requires justification for the very act of borrowing." (citations, mostly to Campbell v. Acuff-Rose Music, Inc. omitted)
The fact that parody by definition must borrow elements from an existing work, however, does not mean that every parody is shielded from a claim of copyright infringement as a fair use. "The [Copyright] Act has no hint of an evidentiary preference for parodists over their victims, and no workable presumption for parody could take account of the fact that parody often shades into satire when society is lampooned through its creative artifacts, or that a work may contain both parodic and nonparodic elements." (quoting Campbell v. Acuff-Rose Music, Inc.)
... we will treat a work as a parody if its aim is to comment upon or criticize a prior work by appropriating elements of the original in creating a new artistic, as opposed to scholarly or journalistic, work.
The court found that TWDG was a parody under this definition, and then proceeded with a detailed analysis of the fair use factors in this specific case. After a long analysis of each of the four fair-use factors, soem of them divided into multiple facets, the court concludes:
We reject the district court's conclusion that SunTrust has established its likelihood of success on the merits. To the contrary, based upon our analysis of the fair use factors we find, at this juncture, TWDG is entitled to a fair-use defense.
It should also be noted that this was a preliminary finding on the status of an injunction, and the actual infringement case was settled, rather than tried.
The case of Suntrust Bank v. Houghton Mifflin Co establishes that for US copyright purposes, a parody is a work that is intended "to comment upon or criticize a prior work by appropriating elements of the original in creating a new artistic, as opposed to scholarly or journalistic, work." A work imitating but neither commenting on nor critizing a prior work is not a parody of it. Such would be the case of the songs described in the question.
The Suntrust case also establishes that while a parody will often be a fair use of the original, this is not always nor automatically the3 case. The full four-factor fair-use evaluation must still be made, and not all parodies will pass. Still less will all works that imitate but do not parody the original.
Parody in non-US law
The Suntrust case is all about fair use, a very specifically US legal concept. It does not exist in the law of any other country that I know of.
The UK and several Commonwealth countries have "fair dealing" a somewhat similar but more restrictive concept, which moreover is not exactly the same in the various countries that use it. Some of these specifically mention "parody" as a permitted purpose of fair dealing. Others do not, but mention "criticism" of the original work. A parody may be a form of criticism. None of them grant an automatic and all-embracing exception for parodies.
Other countries have neither fair use nor fair dealing. Some have limited exceptions for criticism. In some cases parodies might fit these, but it is surely not valid to say that parody is always an assured defense to a claim of copyright infringement.
Parody typically falls into the protection of Fair Use in the United States, which is an Affirmative Defense (i.e. They can still sue you and as part of your Not Guilty Plea or civil law equivalent you would have to assert that it was Fair Use, which shifts the burden of proof onto you.). Fair Use has strong precedence to Parody (I.E. Writing new lyrics to the Tune Of, ala Weird Al, or Singing popular song lyrics in the style of, Ala Richard Cheese) or Educational Works (i.e. the original Bill Nye the Science Guy had a lot of parodies of popular 90s songs discussing concepts related to the topic of the episode.).
It should be pointed out that while Weird Al does not release music without asking permission from the artist performing the song, this is not required in order to publish a parody song. Weird Al is just a really nice guy and most artists see it as a sign of making it in the music industry. Disney's music, characters, and plots, have been subject of vicious parodies over the years (From South Park's use of a foul mouthed Mickey Mouse as the CEO of Disney espousing the more tasteless side of their marketing departments and corporate situations, to even Disney itself in some bizzare levels of Self-Deprecation (Have you ridden the Jungle Cruise ever?)) and Disney has a notorious streak of over-protection of it's intellectual properties. The good news is, you may not even need to go to court over the matter if they sue you as California has very strong Anti-SLAAP rules (Basically, allows a judge to dismiss the case and possibility of refiling if it's pretty obvious its to shut down critical voice rather than an actual case.). Additionally, case precedent holds that IP holders suing for Copyright Infringement must take into account the likely hood of a Fair Use defense prior to filing suit.