Upon reading Lady Miranda's letter Alexander knew he had to intervene in Galiosos whether he wanted to or not, regardless of his personal opinion on the matriarch of the house.
The potential losses his inaction would cause were too great- be it the forfeiture of the huge market, the sacrifice of the naval ships or even the disappearance of the money Lady Miranda still owed him.
And yes, Lady Miranda did still owe Alexander about half of last year's purchases- which she had brought with credit, not cash, promising to repay him once she sold the products.
Thus the question here was not whether Alexander should help Lady Miranda, only how.
And the first solution that came to Alexander's mind was the simplest one- using force.