I'm a bit confused here, so maybe the title is not worded well.
Achashverosh let Mordechay write the letters to his own wording:
"ואתם כתבו על־היהודים כטוב בעיניכם בשם המלך"
And you may further write with regard to the Jews as you see fit.
Mordechay [and Ester] wrote the following:
"אשר נתן המלך ליהודים אשר בכל־עיר־ועיר להקהל ולעמד על־נפשם להשמיד ולהרג ולאבד את־כל־חיל עם ומדינה הצרים אתם טף ונשים ושללם לבוז"
...they may destroy, massacre, and exterminate its armed force together with women and children, and plunder their possessions
And that phrase seems contradictory to me: killing women and children is only allowed in the War of the 7 Nations (inc. Amolek) but then their possessions are forbidden (see Shmuel A-15).
So did Mordechai declare an obligatory war on Amolekites (that would include women and children) but why allow their possessions, and if not Milchemet Chovah - why kill women and kids?