This is a topic that David and I have had a great deal of fun with over the years, possibly beginning with a discussion of Dead Poets Society
[sic; note lack of apostrophe], which is one of his favorite movies.
The fact is that I find these holiday names rather arbitrary. If you buy a calendar in the United States, you will probably see these days highlighted:
- Mother's Day (singular possessive)
- Father's Day (singular possessive)
- Children's Day (plural possessive)
- Veterans Day (plural non-possessive, thus apparently attributive)
Why does "Children's Day" stand out? Because the word "child" has a non-standard plural in English. (As you say, it does not end in "s".)
If "Children's Day" were to follow the pattern of "Mother's Day" and "Father's Day", it should be "Child's Day". Apparently the person who named "Mother's Day" was either functionally illiterate or intended that only one mother on the planet should be honored on that day.
On the other hand, if "Children's Day" were to follow the pattern of "Veterans Day", it should be "Children Day". But this never happens. In any such structure where the plural form of the noun is irregular, it needs to be written as an obvious possessive.
Thus, we also speak (rather, write) of the Teamsters Union (no apostrophe) but the Longshoremen's Union (with apostrophe). These examples, in my humble (right!) opinion, make it clear that these attempts to justify lazy omissions of apostrophes by reclassifying them as appositives are exactly that.
However, no one can argue against the fact that, ultimately, usage makes correct. The appositive construction that David speaks of is well established, and for the most part, it works.
It also provokes questions from people like Yoko from time to time. As it should. C'est notre raison d'etre.