。
She wouldn't let him touch the baby.
Literal
She [topic-は] him [to-に] baby [to-に] not-let-touch.
A causative-permissive sentence with two に's. 触れる ('touch') takes the touched thing with に — 赤ちゃんに触れる ('touch the baby'). The causative 触れさせる ('let/make touch') with negation 触れさせなかった ('didn't let touch') marks her refusal to permit. The other に on 彼 marks the causee — the one (not) made/let to touch. Two に's stack here: agent of causative + target of touching.