Every Eligible Girl in Rune Factory Frontier has her own Story. Some are linked to the main plot and the defeat of Gelwein, for example, is an intrinsic part both of Mist's story and of that of Iris.
Uzuki's tale is not connected at all to the main plot. Her quest in Trampoli is a search for her missing Elder Brother. It is only in completing her Quest that she discovers the importance of Trampoli in her own life.
For me, it is the character of Tsubute that makes Uzuki's character and 'Story' appealing. I almost would marry Uzuki simply in order to bring the faithful retainer into my household, although the implication in the Congratulations he makes on the occasion of my character's wedding to any other Eligible Girl is that he considers me to be nothing better than a 'ruffian'.
In any case, here is the conclusion to Uzuki's Quest: