Rabbi Judah said in the name of Rav: Just as when the month of Av comes in, we lessen our joy so when Adar comes in, we increase our joy.  (Bab. Tal. Ta'anit 29a).

Strangely, our family has two deaths occuring on the first day of these two months. 

Grandpa Weisberg's death was on Rosh Hodesh Av, when the sages proclaimed that our joy is lessened.  Dad's day of death was Rosh Hodesh Adar, when the sages say that our joy is increased. 

One can ask whether this is meant as a passive affair, i.e. because the way of the world is for bad things to happen around the time of the date of the destruction of the temple in Jerusalem (9th of Av), we should expect that in Av, bad things will happen to us as well.  Or is the issue that we make the beginning of Av mournful and introspective by actively bringing our joy down a peg,  viewing Av as a time of introspection and avoidance of joyous events.  This idea is reflected in our observance of the 3-weeks from the 17th of Tamuz until the 9th of Av when we traditionally do not partake of live affairs and other joyous activities.

In the case of Adar, are we inversely, to turn up the joy and find ways to celebrate the coming of the Purim holiday?  Or are we simply to expect that good things are going to happen to us?

We can understand Grandpa's yearly remembrance on the 1st of Av as being relevant in each case, bad things happened to us, and we also enter the month with a modicum of sadness because of the historical context as well as the personal tragedy which we all feel at the turn of the month of Tamuz.  I am ambivalent about the assertion related to Adar.  We are to bring in the month of Adar with joy, but always with the sadness of the anniversary of Dad's death on the very day that we have been accustomed to crank up the joy meter. 

Purim was Dad's favorite holiday and, the various aspects of the holiday - the scriptural reading of the scroll of Esther, the enforced revelry and the general lack of other prohibitions on performing work - all combined to make it the quintessential "Dad Holiday."