She coaxed and cajoled the reluctant child into going to the dentist.

Literal

She [topic-は] resisting child [object-を] soothing-and-coaxing dentist [to-に] brought went.

嫌がる子供 ('the child who dislikes/resists') uses the ~がる suffix for visible reluctance. 宥め賺す (なだめすかす, 'to soothe and coax') is a compound verb — 宥める ('to calm, soothe') + 賺す ('to cajole, persuade') — combining emotional calming with verbal persuasion. 連れて行った ('took/brought [the child] to') completes the action. A very relatable parenting moment.