Just some random mareh mekomos:
(1) The gemara (Shabbos 118) tells us that there is an issur of reciting hallel unnecessarily. The gemara (Ta’anis 28) tells of Rav who came to Bavel and heard hallel recited on Rosh Chodesh. Being unfamiliar with the minhag, Rav was going to stop them. When he heard that they were skipping while reading (i.e. reading chatzi hallel), he let them continue. Based on this gemara, it would seem that reciting chatzi hallel does not violate the issur of unnecessarily reciting hallel.
(2) There are many things which push aside the practice of aveilus. For example, a ba’al bris can shave on the day of his son’s mila because it is his Yom Tov. One may push aside the issur of eating meat during the aveilus of “shavua sh’chal bo 9 Av” if one celebrates the personal Yom Tov of making a siyum (as is regularly done in summer camps).
(3) The Chayei Adam records that he established a personal YomTov for himself to mark the day he was saved from a fire. He celebrated yearly with a seudas mitzvah. The Chasam Sofer (191, 208) concurs with this approach, and suggests that celebrating being saved from a life threatening situation miraculously is nothing less than a chiyuv d’oraysa.
Irrespective of the practical issues, the fundemental question of hashkafa one must ask on this day is whether one identifies the State of Israel as a positive religious value for the Jewish people. And if you answer in the affirmative, I think it is worth considering whether that value is adequetly conveyed in the chinuch our children are given. I'm not giving answers, just raising the questions.