If the Mass is held in the evening, is it possible that they can attend both — or is it that they hold this to be a solemn day and no celebrations of any kind are acceptable?

Possibly, as time goes by they may relax their restriction. I’ve never heard of any prohibition from the Church which prevents any celebrations on the anniversary of a death. If that were true within the Church, few days would allow for celebrations.

I suspect that this may have more of a cultural rather than religious basis. Right now she’s two so she won’t yet understand, being caught up in the celebration on the actual date. For now, at her age, she will enjoy an extended birthday when she gets to celebrate it on two different days. Give this time.

Though it’s one of those coincidences in life, only you would know if you can or should broach the topic with them.

Good luck; maybe time is the solution here. The second year of grieving is known to be the worst, so the 3rd anniversary will end that second year. Possibly healing can now begin and the dilemma will take care of itself eventually.