On the yahrtzeit that completes the twelve months of aveilut for a parent, the full laws of the year’s aveilut apply.[1] In subsequent years, the laws of aveilut technically do not apply on the yahrtzeit. There is an old minhag, recommended but not binding, to fast during the daytime portion of a parent’s yahrtzeit.[2]
The Rama[3] writes that that one should not take part in festive meals even during the night that begins the halachic date of the yahrtzeit. The Levush[4] disputes this ruling based on his understanding of the logic for the yahrtzeit fast – namely, that the yahrtzeit is a day of bad omens for the deceased’s offspring, and one fasts so that the teshuva that accompanies the fast will help protect him. The Levush posits that since this fast has nothing to do with aveilut, there should not be any restrictions on attending festivities the night before. According to the Levush, your situation has a simple solution: The celebration should be held at night, while the somber practices of yahrtzeit should be during the day.
However, the Shach[5] and others maintain that the minhag follows the Rama’s opinion. Although nowadays it is very common to not fast on a yahrtzeit, there is still a minhag to avoid, or at least lessen, one’s participation in weddings, and the Taz[6] posits that aveilut-type behavior is indeed part of the yahrtzeit experience.
There are several grounds for leniency, besides the aforementioned Levush. Many authorities[7] quote the Magen Avraham as saying that the restrictions apply only on the first yahrtzeit, which ends the twelve months of aveilut. Additionally, the Pitchei Teshuva[8] writes that the restriction against participating in a festive meal applies only to the meal of a wedding, at which the intensity of simcha activity exceeds that of other celebrations. In fact, several poskim maintain that even an avel is permitted to take part in a seudat mitzva such as a siyum.[9] Although the Shach[10] cites the Maharil as not allowing a person to eat at a siyum on his parent’s yahrtzeit, that is only when his minhag is to fast. Even then, the Maharam Shick[11] rules that one who accepted the practice to fast may still eat at his own siyum, and in your case, you are the celebrant of the thanksgiving meal.
What, though, is the status of your self-created salvation holiday? The Chayei Adam,[12] who instituted such a holiday when his family survived a fire, says that it is a mitzva to observe such a day. While the Pri Chadash[13] says that the ability to institute semi-holidays ended with the retraction of Megillat Ta’anit,[14] a clear majority of poskim disagree.[15] Therefore, all of the aforementioned reasons for leniency exist in your case, and it is fully reasonable to celebrate your salvation on the yahrtzeit, preferably at night.
However, it is apparent from your question [only partially presented here] that you are understandably uncomfortable with the confluence of these very different days. Therefore, we do not recommend that you move your celebratory day from when you have been holding it to the yahrtzeit. Although a meal instituted on a day of personal salvation is likely a seudat mitzva, one is not obligated to institute it. While it is not a simple matter to undo the institution of such a day (beyond our present scope), this is not a problem for you, as long as you do not move it to the yahrtzeit.
Perhaps it was min haShamayim (divinely ordained) that the date on which you have been celebrating until now does not cause a conflict. Realize that there are no set rules as to when and how to hold such a celebration. Even Purim, after which this celebration concept is modeled, is not held on the actual day on which the Jews were saved. Some well-known “family Purims” consisted of a fast day on the day of salvation and a feast on a different day. Thus, you can continue celebrating on the day you instituted your celebration (or on a different one), so that the celebration and the yahrtzeit do not cast a shadow on each other.