I don't see why tactical considerations would have been important for the Female Founder at that point. She could just as well have considered the war on Alpha lost - but that would not be a major strategic setback for the Dominion. They could always call it quits and come back later to wipe out the Feds and the Klingons. Wiping out the Cardassians would be a nice, solid step along the greater strategic path of driving terror in the hearts of Solids - not to mention a tactically viable goal (it's better to engage in possible things than in impossible ones, as the possibility of embarrassing failure is greatly reduced...).
See i just don't get this.. why wouldn't it be? She wanted to win the battle, didn't she? She gave an unnecessary order (for whatever reason) that resulted in her losing the immediate battle at hand. They were winning the battle before the Cardassians turned on them. Regardless of her motives or what she thought was going to happen after giving the order it resulted in them losing the battle and hence was a mistake.
I suppose you could justify it that she just expected the Cardassians would fall in line after millions of their people were slaughtered.. I don't think it really fits. She's shown that she seemed pretty astute when dealing with the Breen and knew exactly how to minipulate them, but then knew so little about the Cardassians that she cluelessly underestimated them.
It made no sense to me, anyway..