Sometimes a course of action that sounds like a good idea at first seems less attractive upon further reflection. The verb 思い止まる(おもいとどまる)indicates a change of heart. 思い止まる is a compound verb that is formed from the verb 思う(おもう= [think] and 止まる(とどまる)= [stop].
If you want to bring about a change of someone else’s mind or heart, then use the transitive form of the verb, 思い止まらせる(おもいとどまらせる). A closely related word is 抑止 する (よくし する)or “to deter”