。
My sister doesn't want to associate with them.
Literal
Younger-sister [topic-は] them [with-と] [possessive-の] association [object-を] is-not-desiring.
交際 ('association, socializing') is a formal word for social relations. 望んでいない ('does not desire') uses 望む, a more literary verb than 欲しい or ~たい. との is と (with) + の (noun-modifying), creating 'association with them.'