I'm not convinced utilitarian reasoning can always be applied to situations where two preferences come into conflict: Calculating "secondary" uncertain factors which could influence the value of each decision ruins the possibility of exactness. Even in the trolley problem, in all its simplicity, each decision has repercussions whose values have some uncertainty. Thus a decision doesn't always have a strict value, but a probable value distribution! We make a trolley decision by 1) Considering only so many iterations in trying to get a value distribution, and 2) seeing if there is a satisfying lack overlap between the two. When the two distributions overlap too much (and you know that they are approximate, due to the intractability of getting a perfect distribution), it's really a wild guess to say one decision is best.

Utilitarian calculation helps the process, by providing means of deciding when each value probability distribution is sharply enough defined, and whether the overlap meets your internal maximum overlap criteria (presuming that's sharply defined!), but no amount of reasoning can solve every moral dilemma a person might face.