Is there any verb for making a girl more girly?
Solution 1:
I think the problem here is a misconception caused by poorly presented materials. The resource you checked misrepresents the facts a little. It lists two definitions of the word as if there are different meanings, but the second definition really just seems like a specific application of the first meaning. The Random House Kernerman Webster's College Dictionary (©2010) does not make the distinction under its listing for feminize, and although other dictionaries do, I fail to see the distinct need.
Making matters even more confusing is that the resource you probably checked probably did not do a very good job of distinctly formatting it to ensure that the definitions were checked properly.
Suffice it to say that feminize can be applied to females who are not already as feminine as they can be based on societal expectations. For those of you who are doubtful, it should be noted that such women exist, and we even have a word for a certain personality type of that sort, which is Tomboy.
An example of feminizing a woman can be found in Good Times, Bad Times: Soap Operas and Society in Western Europe which was written by Hugh O'Donnell and published in 1999:
At the other side of the spectrum, so to speak, Iris Brandner, Initially a somewhat dowdy housewife wearing uninteresting denim jackets and non-eye-catching jeans, has cast her housewifely burden, modernized and feminized her wardrobe and hairdo, and set about finding her real self in the public sphere …
Another can be found in Cosmopolitan Magazine, Volume 195 (1983) [No preview]:
Her husband, Norman, has had a great influence on how Alexandra dresses. "Mostly it shows in a feminizing of my clothes." she says. “I used to wear really tailored shirts. but now I buy softer ones. His influence on evening clothes is greatest,
Arguably, the object of Feminize is not actually the woman in these cases, but it should also be noted that the clothes are not necessarily feminine by virtue of being worn by a female.
However, the woman can be the direct object of feminization too where appropriate, as exemplified in these contexts:
Reckless Dreamer by Don Alden (©1985)
He feminized her, feminized the valley where her waist joined the round curve of her hips. He was a young man who adored making love to women, and in the process he made them even more beautiful.
The introduction to The Incorporated Self: Interdisciplinary Perspectives on Embodiment edited by Michael O'Donovan-Anderson (©1996)
The hermeneutic encounter may instead imply a mutual vulnerability; thus was Janette's woman warrior able to decapitate (castrate) the baron even as he "feminized" her with his intrusive gaze.
Finally, it should be noted that we do have a word specifically for making males less masculine or more feminine, and that is effeminize from effeminate, at least according to Merriam-Webster, although it should be noted that it is is at least implicitly derogatory since it implies that the male is not as manly as he should be.
Solution 2:
Checking usage on the internet, it seems that the meaning of girlify and girlification depends very much on the context and the point of view of the speaker/author (see below).
However, there does seem to be a narrower word that fits what you want to express. It's less common but I don't think it would be misunderstood.
princessify
I found two definitions of princessification. Both sources omitted to include a definition of princessify but I say, if we can have princessification, why not princessify?
princessification: (informal) The process of making or becoming girly or hyperfeminine. (wiktionary)
You could also use hyperfeminize if you don't mind the perhaps clinical sound of the hyper- prefix.
Parenthetical note: Here are some examples of varied uses of girlify and girlification (there are plenty more -- the variety is pretty endless):
Polly Toynbee recently gnashed her teeth over Girlification's triumph over Feminism. https://www.notesfromtheslushpile.com/2008/04/polly-toynbee-on-girlification.html
Girlify (def.) - take something ordinary and turn it into something feminine and pretty. http://littlebungalowbythebeach.blogspot.com/2013/03/girlified-man-shirt.html
The writer never does get around to explaining how girls should girlify if they want to snag "good (meaning marriageable) men." https://www.rgj.com/story/opinion/voices/2017/07/26/cory-farley-freelance-writer-who-lives-verdi/513548001/
verb To make girly. https://www.wordnik.com/words/girlify