Reason with your wife in a CALM, RELAXED, GENTLE, MILD-TEMPERED manner. Ask about wedding anniversaries, and why they CAN be celebrated because "marriage" was instituted by Jehovah, correct?
Well, Jehovah certainly instituted birth, did he not? If we count the number of years we are married (technically speaking, we should not count any years at all if we are destined to live forever in a paradise, right?)then what is wrong with counting the number of years one is alive?
If a wedding party is appropriate (with ritualistic pagan chicken dances)with music, food and gifts, then why can't children celebrate with games and presents, too? I personally do not see the difference.
I know, they will quote ECC 7:1, better is the day of one's death than the day of one's birth and a good name is better than fine oil.
However, what is that scripture actually saying in the context of that chapter? What is the basic theme running through most of Solomon's writings? Generally it is "futility and brevity of life", not whether or not you can rejoice or celebrate any particular event.
Also, the Pharoah's birthday, explain it's relevance? Just because a biblical character who is an unbeliever commits a sin does not logically justify the establishment of "new" bible principle. For example, if Delilah cut Samson's hair, and then he was compromised and captured, doe that make all haircuts bad?
Since when do we modify our judgment and thinking and power of reason according to the actions of unbelievers? Are their lives our thermometer in life? Of course not.
Try reasoning and pray if it helps. Best Wishes!