Whether the words are capitalised has no bearing on the fact that Parents' Night is the object of the preposition.
What makes you think that? What do you mean by "In the book"?

Student or Learner
Hi,
About this sentence "The science lab was displayed on Parents’ Night."
In the book "Parents' Night" is an object of preposition because “Parents'” is written with a capital P. If I changed P to a lowercase to form an adjective, would that violate any grammar rules?
Whether the words are capitalised has no bearing on the fact that Parents' Night is the object of the preposition.
What makes you think that? What do you mean by "In the book"?
Something is wrong with uploading images... hmm
Can anyone see the image?
I would assume "Parents" would modify night so it would class as an adjective. But then I looked at the diagram and it shows it as an object. According to the diagram it describes "Parents' Night" as an object. In the sentence given, "Parents' Night" is an object is that right?
It's been almost fifty years since the last time I diagrammed a sentence, but I think your diagram is incomplete. Parents' Night is, I think, a noun phrase which serves as the object of a preposition. In that noun phrase, Parents' is an adjective modifying Night.
I am not a teacher.
"The science lab was displayed on Parents’ Night."
"The science lab was displayed on Friday night."
"The science lab was displayed on the last night."
"The science lab was displayed on Friday."
In each of those sentences, the underlined phrase/word is the object of the preposition. Only in the third is there an adjective, 'last'.