When Winnie goes fishing with Miles, she kills a mosquito but asks Miles to let the trout go free. Why would she do that?

She does that because Winnie is just like many other animal loving human beings.  I'll use an over the top stereotype as an example.  Let's assume that we know somebody that is a member of PETA and a fully fledged vegan.  By all accounts that person believes in and respects animal life.  But I'm willing to bet that he or she still uses antibacterial soaps and cleaning sprays.  I'm sure when they get sick, they take antibiotics.  That guarantees the death of millions of bacteria.  Or, if that person has an ant infestation in their house, I'm sure that some ants die in the process of getting rid of that invasion.  Lots of tiny little animals die in the process.  The thing about larger animals like a fish in the case of Tuck Everlasting is that it is easier to imagine yourself as it, or it as a human being.  It is easier to sympathize with the animal's plight and repercussions of its death.  Winnie also possibly is thinking that the fish never did anything to hurt her or another human, while the mosquito is much more antagonistic to people, so its death is more justifiable.