。
She hinted that she wanted him to leave.
Literal
She [topic-は] him [to-に] go-back [want-to-have-てもらいたい] [quotative-と] hinted.
~てもらう is the receiving auxiliary ('have/get someone to do for me'); ~てもらいたい adds the desiderative ('want to have/get someone to do'). So 帰ってもらいたい = 'want (him) to leave (for me).' The と quotes this internal wish as the content of the hinting. ほのめかす ('hint, imply, allude indirectly to') is the verb of indirect communication — perfect for situations where a direct request would be awkward.