the sentence "I persuaded him to go there" can mean just the option 1 or can mean both 1-2
1- I wanted him to go and he accepted after some talks
2- I wanted to go and he let me go after some talks
the sentence "I persuaded him to go there" can mean just the option 1 or can mean both 1-2
1- I wanted him to go and he accepted after some talks
2- I wanted to go and he let me go after some talks
Sentence (1) is the correct meaning.
Sentence (2) is not the correct meaning because the verb “to go” applies to “him”. You could get the meaning of sentence (2) by writing “I persuaded him to let me go there.” Here “to let” applies to “him” and “go” applies to “me”.
Arguably you could get the meaning of sentence (2) by claiming that the “to let me go” clause applies to the whole of the main clause. (ie the reason I persuaded him was so as I could go there.) This is the same grammatical structure as the sentence “I killed him to steal his money.” In context with the meaning of the word “persuaded”, you example would always be understood as having meaning (1).