If one forgets to say Retzei or Yaaleh Veyavoh in the third beracha of Birchas Hamazon, there is a special text of the beracha which should be recited provided one has not yet begun the fourth beracha. If one has forgotten Yaaleh Veyavoh in the beracha of Retzei in the Shemone Esrei and reminds himself before beginning the next beracha of Modim, there was a big dispute among the Baalei haTosafos what to do. Rabbeinu Elchonon was of the opinion that in davening the din should be the same as in benching, that as long one has not yet begun the next beracha, one can recite Yaaleh Veyavoh. Initially the father of Rabbeinu Elchonon, the Ri Hazokein, disagreed with his son for various reasons and felt that it is improper to recite Yaaleh Veyavoh in between Retzei and Modim. But at some later time, the Ri was davening in Paris next to his uncle, Rabbeinu Tam, on Rosh Chodesh, and he overheard Rabbeinu Tam failed to mention Yaaleh Veyavoh in Retzei and insert it before Modim. From that time on, the Ri followed the view of his son, Rabbeinu Elchonon. The Vilna Gaon, in his commentary on Shulchan Aruch, has adopted the initial position of the Ri, but the generally accepted view is like the Rabbeinu Tam and the Rabbeinu Elchonon.
What if one forgot to say Al Hanissim in the beracha of Modim and reminds himself before starting the concluding beracha of Sim Shalom? Should the din of Al Hanissim be the same as Yaaleh Veyavoh? Or, if one forgot mashiv haruach umorid hageshem in the middle of the second beracha of the Shemone Esrei, would it make sense to insert that line before Ata Kodosh? Rav Soloveitchik pointed out that there is a major distinction between mashiv haruach and Al Hanissim on the one hand, as opposed to Yaaleh Veyavoh on the other hand. Mashiv haruach and Al Hanissim were initially instituted by the Chachomim as part of a long sentence in the middle of a beracha. The commentaries on Shulchan Aruch point out that the correct text both in Shemone Esrei and in benching should really be : Val Hanissim. We thank Hakodosh Boruch Hu for a number of things and then additionally say Val Hanissim, i.e. we thank Him for the miracles as well. (It would appear from the Rambam that on Chanukah and Purim we add Val Hanissim into the Shemone Esrei right after the words "erev veboker vezohoroyim" so that it flows to the end of the long paragraph; it does not really make sense to first say "hatov ki lo cholu rachamecha...", which is really summing everything up previously mentioned, and only afterwards to add on Val Hanissim.) But Yaaleh Veyavoh, both in Shemone Esrei and in benching, as well as Rzei in benching, are not added as an elaboration and a elongation of the paragraph. They are actually an inserted self-contained and independent paragraph in the middle of the beracha. So, although the common practice is like the Rabbeinu Tam and the Rabbeinu Elchonon that Yaaleh Veyavoh can be recited in between Retzei and Modim, this should not really be so with respect to mashiv haruach or Al Hanissim, since these were initially instituted as an integral part of the beracha.
Different explanations are given as to why there is no mention of Chanukah or Purim in Al Hamichya. Rav Soloveitchik used to give the following suggestion. Val Hanissim was initially instituted in benching as an elaboration on the theme of hodoya-thankfulness, and as an elongation of the beracha and beginning with a vov, i.e. Val Hanissim (as explained above). But Al Hamichya is referred to in the Gemarah as Mei'ein Shalosh, the abridged form of the three berachos of the benching. In the abridged form it is self-understood that one leaves out the elongation of the beracha. But mention of Shabbos, Yom Tov, and Rosh Chodesh was always an insert into benching and was never formulated as a longer version of the beracha, so therefore, even in the short version, it was required to mention Shabbos, Rosh Chodesh, and Yom Tov.