It's amusing that your entire argument as to why Ashe is unable to control her emotions is based on one scene in the entire game.
Let's put some perspective on this:
Ashe - 17 years old:
- several brothers killed in war
- husband from an arranged marriage killed in war
- father assassinated by seemingly her own people
- faked her own death and became the leader of an underground resistance movement
Ashe - 19 years old:
- suffers from betrayal from her own people at least twice
- had the fate of an entire nation of people resting on her shoulders (with a population far bigger than both Tifa or Selphie's losses combined)
- deals with all of this in her stride and then in one scene, ONE SCENE - slaps the person she thought killed her father rather than running him through with her sword right there on the spot - apparently this makes her overly emotional.
- averts an unnecessary bloodbath at the very end as her guiding motive throughout was for her people rather than getting revenge
Selphie - 17 years old:
- Fails at stopping her home being destroyed. Gets emotional over it. Remains emotional.
Tifa:
- See's her hometown massacred by one man as a child - vows vengeance
- Engages in terrorist activities against an organisation as part of said vengeance killing innocents in the process and leaving thousands of others without electricity and probably other basic resources
- Eventually, through a male character, realizes that blind vengeance isn't the best motive
Ashe dealt with far more than the other two combined and remained emotionally stable for far longer than they did. From a very young age Ashe has had to deal with death, betrayal, conspiracy and then at age 17 (when the other two were busy falling off of cliffs or serving alcohol) got thrust to the role of leader of her under siege nation.
You must've played a very different Final Fantasy XII.Ashe she spends like 99% of the game grieving over her husband.